bike going wobbly? sounds like shimmying (sp). Typically happens at high speed and on corners. To stop the bike from shimmying, stop pedalling and press both legs onto the top tube of the bike. The legs act as a damper and will smooth out the shimmy.
Make sure your head set is on tight, see that the wheels are true..
As someone said, put your weight toward the back when you have to hit the brake. This will keep you from getting the feeling of doing the endo (end over -- flipping over the handle bar).
Practice riding behind an experience rider to develop your confidence.
The exception being on hills with hairpin turns (like the one over at Shannock Hill Road.) I do take it easy on short steepies. I don't trust the SUV drivers on cell phones who seem to perpetually lurk middle-of-the-curve on those roads. But I still get in the "stance", just hold my body up a little more to catch the wind to keep me slower.
I can do five more miles.
In my experience, once you've spent a summer getting over your fear of going down hills on inline skates, you lose most of your fear going down them on a bike.
The most important advice I got from skating was: don't forget to breathe.