HH- I am growing out my bangs as we speak and they are now chin length. How short are yours? I know that when I first got mine, I had the same problem with keeping a curl after wrapping it, but as they grew longer it became easier. When they got the nose length, I didn't have to bother bumping/curling them in the morning. My bangs grew/grow pretty fast so it didn't take long. It shouldn't take you YEARS to grow to yours to ear nor jaw. My guess (depending on your normal growing pace) would be anywhere from 4 months-6months. Again, how short are they now?
I wrap my hair every night in the same direction and have not had a problem, but using heat everyday on your bangs is def not good. I like the idea someone gave about popping a curler or two in your hair as you are getting ready. That should help.