I’ve had hot water recirc in houses in the past. Was very satisfied with the results (no water waste, no time waste, negligible operating cost).
As above a timer can reduce the hours of operation. Even if you leave it active 16 hours a day, you’ve still knocked 1/3rd off the annual cost, be that large or small.
You can recirculate just the one bathroom, or try to recirc the whole house. The more run(s) you recirc, the greater the heat loss. Any hot water pipes that are new or are in walls you’re opening up anyhow, or are in basement areas, can be insulated. They sell foam rubber 3’ long tubes slit lengthwise for just this purpose. I DIYed installing those on the hot water runs in the accessible parts of my basement. Little cost, little effort and as a bonus the hot water at the other end of the house was noticeably warmer.
Here’s some relevant history on instant hot, recirc, and heat waste: