I have the same problem as bounceswoosh except with my road bike. If I'm in a small group where people will wait for me, I try to take the hard climbs at a rate that I can stay on the edge of going anaerobic. But, if I'm on a big group ride, I find that I will push myself into that panting, gasping state just to try not to get dropped.

One side effect of this is that, as we crest the hill, they all take off and I'm still panting too much to put it in high gear and build up a lot of speed right away. Any tips or techniques I could use to improve in this area? Or will I just find that if I stick with it, I will build the aerobic fitness over time?