I did this for years. I would pitch a couple degrees below target, and swap frozen water bottles at least twice a day. I found the temp of the water in my tub was pretty reliably within a degree or so of the fermometer reading. As you've noticed, the trick is to change those frozen bottles for the first 3 days or so to try to keep the water at your target temp. After 3 or 4 days (average strength ales), I took the fermenter out of the water and allowed to warm up to room temp until I reached FG, to help the yeast attenuate and clean up. It takes a commitment those first few days, but I got good results.