My bathroom is ridiculously tiny. A very pregnant visitor once asked if she could use the bathroom. "You can try." We do have a full bath, but no room to house a baby bathtub. When my son was born 5 years ago and now with my daughter, we made do with other products suited to small homes. Here they are...
With my son I used a foldable bath sling similar to this one above by Summer Infant. It was about $10 and, once folded, was small enough to stow away above our medicine cabinet. There was nothing fancy about it and I always kept one hand on my son to make sure he didn't slide off, but it did a good job of keeping his head out of the water. When he was around 5 months old I gave it away to another family and would simply put him in the tub, in a few inches of water (now, with more confidence as I had more parenting experience).
For my daughter, now almost 4 months old, I bought this froggy "bath cushion" by Safety 1st. It was also less than $10 and easy to store above my medicine cabinet. After a bath I wring it out, leave it at the end of the tub and it dries completely within a few hours. I was worried it might develop mildew over time but this hasn't happened so far.
I know some parents who forgo a baby tub use their sink (sometimes in conjunction with a Puj Tub), but my bathroom sink is teeny tiny and I didn't want to rearrange the dish rack and other kitchen items around the sink each time I wanted to give my baby a bath.
I recommend both these products for small home dwellers or as something to travel with or keep at grandma's house. Did you skip the baby bath tub? What worked for you?