I don't mind a few bruises, I've already gotten quite a few from my other days out. I just don't think anyone HAS TO do something they aren't comfortable with(especially a beginner).
The heartless bastard answer would be to stop boarding if you aren't comfortable with it.
But since the real MunkySpunk is indisposed at the moment and this is his good twin, two main things:
1) Learn to fall. Keep your hands in loose fists, punch down with a slightly bent elbow to catch yourself instead of hitting the ground open palm. Absorb the impact by using the flex of your elbow and shoulder as a shock absorber. You'll have a much slimmer chance of breaking your wrists when you fall. Tuck and roll with the fall
... don't resist it. Using a car analogy: It's much easier to swerve out of the way of an accident than to slam on your breaks and pray you stop in time. Landing on your ass cheek was good, a bruised glute is much better than a broken coccyx.
2) Don't bail. Have faith in yourself and your own abilities. Take a deep breath and tell yourself that instead of going 'Oh SHIT! I'm going faster than a walking pace, time to panic and fall!' you're going to say 'OK, this is the speed where I should find transitions much easier, hang in there for 20 more feet, swivel those hips, and find my edge control.'
Some people here will talk about board flexion, minding your center of balance, initiate a turn with a slight press of the toe, and a million other things to keep in mind while you're in a state of near panic about hurting yourself. Don't worry about remembering any
of that right now - you'll overload yourself and just make things worse. Remember only two things right now: stay up instead of a panic and bail, and roll with the falls. Get your turns linked at something resembling speed, get comfortable with it, and then worry about the millions of details later.
You don't have to bomb a run, but you DO have to get some velocity. If you don't push your own envelope, it will never grow.
If it's important enough to you, stick with it and you'll get it.