Are you currently, or do you plan to be, leasing a school horse? If so, ask your trainer/barn manager, whoever is in control of the horses.
Unless there is a conflict between the leaser and another student, then it should be fine for you to just use the normal bridle and schooling saddle as usual. If your rides are at different times, just switch the saddle. If you're riding at the same time, then it's a little more complicated. Just ask the trainer- if there is a really big issue, then buying your own saddle may be an option.