Your fingers shouldn't be working any harder than if you were just tapping them on your leg. If they are, you need to practice your technique. Are you pulling the strings, or letting your fingers roll off of them?
Being new, this the best time to learn to play with a light touch as it will ultimately give you the most versatility as a player. Practice air bassing on your leg, a table, or whatever. See if you get tired just as fast. If so, then air bass all day long until you build up stamina
. If not, then work at adjusting your technique.
As with anything else, the more you do it, the easier it'll get.