I play guitar.
Now that that's all said and done, I can play bass with a pick, but I can only play for about a minute with my fingers. After that, they get so tired, and they get pretty useless. Does this happen to everyone? I'd imagine it builds up over time, but are there any specific exercises to combat this problem?
Just play a lot. You could just sit and pluck an open string for a while every day until it's easier.
When I started, I used the pick all the time, but now I rarely do unless I think the song calls for it. It will come faster than you think. You might pick a song or two to work on with your fingers and practice until you're comfortable with that song or those songs. Then add a new one. Before you know it, you'll be used to using your fingers.
Well we all shine on--like the moon and the stars and the sun.
-- John Lennon
Try to relax. I know that I sometimes use too much force with both hands/fingers, but it's not really necessary. Those heavy strings seem to beg for more effort. You can pluck with a very light touch and it will sound fine. Fretting can require more force, but a good set-up can help that too.
get a hand excerciser, I play bass for my band and we play some pretty grueling 3+hour straight practices like 3+ times a week and my hand used to go dead after about anhour, and it didnt get any better, then I got one of those hand squeezy things with the springs and I do that about an hour or 2 a day in the morning, so my hands have time to rest up before I play and after like 3 weeks of that I could play for the 3 hours straight and not even feel it in my pick hand, and my bass lines are FAST hehe. Hooked On Squeezy Worked For Me. Also, ive heard good sucess with rubber balls for pro players to squeeze as it hurts your hand less than the spring device but I havnt tried it yet.
SHUT UP ABOUT IRON MAIDEN SOLOS AND GO PRACTICE!