My experience (25 years) with bromine has been that the chlorine in the product does serious, expensive damage to covers, pillows, and pump seals. Read the label on your tabs: most are 44% available CHLORINE, and that is hard on everything. I try my very best to talk people out of using tablet bromine.
If for some reason you absolutely must use bromine, use "Brilliance" brand. It has no chlorine built in. You will need to shock the tub with an oxidizer once a week, but you should be testing once a week anyway, so it's really no big. Why test once a week? Because a floater is NOT an automatic device: you can heavily overdose a tub and for some reason people don't take the floater OUT when that happens...
HTH