You may or may not hear it at 10 weeks. No, you don't need a full bladder.
Don't worry if you don't hear it because it's not uncommon. If you're thin, that helps to hear it earlier. I have a uterus that tilts quite a bit toward my back so that's a factor for me. They can never get mine this early.
If they don't hear it, maybe they'll do a super quick u/s just long enough for you to see the heartbeat to put your mind at ease. Let us know when you get back!