A general rule for storing bread and buns is never to store them in the fridge. This causes the bread to dry out a lot quicker.
The very best thing to do is to freeze it and get it out to defrost on the day of eating. Bread can easily be sliced before you freeze it, so you can get out what you need when you need it.
Another way of keeping bread really fresh is to freeze it before it has been baked in the oven. If you are making small bread rolls, for example, freeze them on a baking tray once they have risen and before baking. When you want to serve them, simply remove them from the freezer and turn the oven on. When the oven is up to temperature, put the rolls in and serve them freshly baked.