Once a day
I change out the bath sheet once a day. Usually I just shower in the morning, but if I take a second shower in the afternoon (after a hard day at work or in the garden or home shop) I'll generally use the same towel I used in the morning. But then the next morning the bath sheet goes in the hamper and a clean one put in its place on the towel bar. I have seven such bath sheets so it works out OK if I launder them once a week. But usually I'll do a load when I accumulate five or six bath sheets, cause the Neptune doesn't like to do a full seven.
In the kitchen, I keep the dish towel and hand towel on opposite towel bars on either side of the sink. I change those out as needed, generally every 2-2 days, more if they get dirtier faster.
All the towels get washed in hot water: the bath sheets at 130F in the Neptune, and the kitchen towels at 160F in the Miele 1918A (along with white socks, white t-shirts, white y-fronts, etc). I've measure the temp in that washer and 160 F turns out to be more like 155F, but that is still plenty hot to "sanitize" everything. I've tried the 170 setting but it seems to be a bit too hard on the elastic in the socks and briefs.
Prior to my induction into the world of laundry aficionados, I probably used the same bath towel several days in a row. But I like having a clean, fresh smelling towel in the morning, and the Neptune is relatively energy and water efficient, so why not?