You don't say if it's a normal, sports or nursing bra. With a normal bra, you should wear your bra as long as you would any other under garment (singlet, camisole etc...) but a guide should be to wash it every 2 days by hand in a gentle hand wash product. If it's a sports bra, you should not wear it again until washed. If it's a nursing bra I would recommend you wash this every day as it would become soiled from milk leaks and could possibly smell. Never heard of infections got from dirty bras though.
You can wear the same bra continously for two days, it may not affect the irritation to you. You have to change it every two days or you can wash the same and wear it again after it dries.