OP, public pools dont really exist , most hotels, condo blocks, moobaans have pools for residents so there is no demand. Any place that is running a business charging for pool access wont be 40 baht, more like 100-200 baht. You may be able to find a condo block you can sneak into but usually involves paying the security guy. 99% of places wont just let you wander in, as others are saying.
Why not move somewhere that has a pool, it would ultimately be cheaper than paying for access/transport each day.