Is it only the bathtub that's freezing or your entire bathroom? I usually just run more hot water when my tub starts to get too cool. It sounds like more of an insulation issue than a bathtub one to me. Basically if you have a cast iron tub and it's cold before you add hot water, it will considerably reduce the temperature. It's like when you pour hot water into your tea cup and let it warm up the cup, then dump that water and add the tea—it keeps it hot. Of course the volume difference between a tub and a teacup is huge so that method won't work. But if you make sure your bathroom is warm and the tub is as warm as it can be before adding any water, maybe even turn on a space heater near it—that could help.

The first thing to do is check and see if there is a gap of some sort between your floor and the parking garage that is letting cold air in under the tub. Have you had any trouble with pipes in the wall freezing? Does the bathroom floor also get cold? Does the tub get warm in the summer?

If there's no air gap, then you probably have insufficient insulation between the garage slab and your floor. If this is the case, the slab is basically a thermal mass that is radiating heat or cold into your bathroom. Apart from pulling your tub out and adding insulation, I'm not sure what to tell you.

Do you own or do you rent because that will make all the difference in the world as to the answer. If you rent, you may want to put down rugs and mats on the bathroom floor. You might also be able to rig up some sort of insulated box to place directly underneath the tub (filled with either styrofoam, packing peanuts, or actual insulation). Plus this will probably look better and be less conspicuous than any sort of tub surround.

If you own, you might want to replace the flooring, insulate the floor, and add underfloor heating.

Quick fix:
Fill a tea kettle or large pot, and bring to a boil (1-3 minutes.) Pour into tub -- drain closed. Boil a second kettle. Empty tub. Fill tub from faucet. Add hot water from towel-insulated kettle as needed during bath: pour away from tender body parts! Use warmed towel after bath.

An old ceramic tub where I used to rent had this same problem, and on a cold winter's night I'd do what trishdom suggested - run some hot water, wait 15 mins, drain and refill. Easy fix! I don't see why it should affect your bubble bath enjoyment.

Like others said about running more hot water. Don't just run more hot water, run ONLY hot water. When it's cooled down to a tolerable temperature (which should happen with a few minutes if youre telling us it's getting cold too fast) then you get in. Once you're in, if it gets too cool, let some water out, run more hot water in.

oh and chances are if the bathrub is freezing, your whole bathroom is freezing. Which can be resolved only through heating the room. Insulation will allow you to heat the room less to maintain the same temperature.

I second the two-kettle fix. I rent and have an iron tub and a water heater that isn't exactly large. I pour two (sometimes three) full kettles of boiling water into my tub before even turning on the faucet. Then I run the usual tub full from the faucet (hot water only cos I like to lobster myself) and get in once it's full. The boiling water helps warm the iron tub and the cold-ass tub helps cool the boiling water. Works out well.

Until the building management can re-insulate the space beneath your tub, I'd try a space heater facing the tub, turned on for 30 min before running a bath. Either that or an aquarium heater :)

Depending on the tub enclosure you can insulate under the tub and not worry about the whole floor. Drill a small hole where the back of the tub meets the wall (if it is an apartment-grade fiberglass tub-surround) and use spray foam insulation to fill the gaps and keep the tub warm.
If budget isn't as big of an issue and you clear it with your landlord (if you rent) you could convert the tub to a jetted tub and that includes a heater for the circulated water.

If you're renting an apartment, the building owner isn't going to insulate the ceiling of the unheated garage...
...and if you're in a condo, the Homeowner's Association would have to charge a special assessment to all owners to insulate the garage ceiling.

Run more hot water.

thank you to everyone for your advice!

and, to clarify... 1.) we are renting. 2.) the bathroom overall is warm, it is only the tub that is freezing.

my apartment tub was the same one. It was one of those large oval soaking tubs and try as I might the water was never warm enough by the time it was full. I started placing my space heater in the bathroom about 15 min before I was ready to bathe, aimed right at the tub and that seemed to do the trick, a couple times on particularly cold days I had to use the tea kettle method. That bathroom was terribly insulated though.

Preheating your tub with boiling water from a kettle is a great trick, too.

I would think an induction cooktop would be more effective than a kettle.... you would warm up a bigger volume of water in one shot and probably faster (and less expensively). If bathing in a tub is that essential to you, I would probably invest into a small induction cooktop. I am not sure but I think they are in the neighbourhood of $150?

I like this idea, similar to what my grandparents used to do to heat the bed in winter: once tub is full "place 3 large stones that were baked for 15 minutes at 350 degrees in the tub".

I used to live in one of the coldest towns in the US, in a little old house with an uninsulated bathroom, but a wonderful cast iron tub. I'd preheat the tub with a few inches of hot tap water, which would also be enough to get the water heater to kick on. In 15-20 minutes, I would drain, then refill with the extra hot tap water--the water would stay nice and warm for a good long soak.

When we installed a new tub, we sprayed "Great
Stuff" foam insulation to fill the cavity around the tub. You could also spray foam insulation on the surface of the underside of the tub.

Can you wrap the outside of the tub in an electric blanket or those under-the-carpet heated panels? I'd also put up a nice thick shower curtain to keep the air around the tub steamy.

What about heating some massage rocks and adding them to the tub? If you know you are going to have a bath at the end of your day you could even heat them in a crockpot on low all day and then add them into the tub as needed.

i have had this problem with pretty much every old house i have lived in. cast iron tubs aren't efficient for baths unless you know the tricks, if you heat it up right, the water will stay really warm.

step 1. without any water in the tub, put a space heater or two aimed at the outside of the tub shut the bathroom door and leave it for a little while.

step 2. boil two pots of water and pour them into the tub (it is best if you pour it down the sides as well as into the bottom)

step 3. fill up the tub as usual. the warm metal will keep your bath water hot for a nice long bath.

I use an econoheat square. it is like a concrete slab that gets hot. its cheap. the heat transfer not only warms the tub,but the whole tub heats the room.I stick it right in the tub all day and night when its cold.