Mice can easily climb up things such as counters, tables etc and can even climb into cabinets to get into food you have in there.
So if a mouse can easily climb up walls, counters, tables and cabinets that means that mice can easily climb into your bed when you're sleeping.
If you notice mice around your bed you should place a mouse trap near or under your bed to prevent the mouse from getting into your bed.
If mice do climb into your bed then the mice could bite you and cause some diseases so always place some mouse traps near or under your bed if you have mice in your home or in your bedroom.
I've had a mouse climb into my bed before and it actually did bite me but luckily I didn't get sick even though I had a doctor check it out.