Seeking pool advice from Houstonians who swim regularly

I‘ve recently moved into the city and I’m in need of a good lap pool to hit before work. There have been similar posts on here in the past, and I have taken some advice from them to try out a few. Here’s the snag, however: I don’t drive and it has certainly been frustrating travelling to those pools via bus. I live in Bellaire and work in the Museum District. What pools do you recommended within this stretch or nearby? And on the off chance, if there is anyone who knows how I can finagle a Rice Recreation Centre membership as a non affiliated person, please do let me know. That pool is the dream!