I think there are two things you'll need to work.
1. Do hill intervals.
For these, start in the biggest front chainring and the smallest rear cog. So if you have a front 34-50 and the rear is 11-25, your first interval is 50-11. After each interval, rest for approximately 1-2 minutes (including the time back down the hill), then move over one cog in the rear and do the next one until you've done all 8-10 cogs. So you'd have something like:
50-11
50-12
50-13
...etc.
50-25 (assuming there's no cross-gearing problem)
When you get good enough at that, go back the other direction (so move to smaller and smaller cogs every interval ) for a total of 16-20 intervals.
2. Sustained power
The problem with doing short hill intervals is that while they build your power and climbing ability, they don't prepare you for long, sustained climbs. So you need to be able to handle riding at your lactate threshold (LT) for an hour or more. If you don't know your lactate threshold (look it up online and there's tons of easy tests you can do to determine it), you can estimate it as 85-90% of your max heart rate. "Most" people fall in that range.
Start with 25 minutes of riding at your lactate threshold without even 10 seconds of falling below the range (so if your LT is 90%, you need to give yourself a range so make it 85-90% of your MHR). Each week, add 5 minutes until you're doing a full hour straight. If you don't have a good loop (with no stop lights) where you can do this, find a road where you can ride 5 minutes without any stops and just go back and forth on it.
Hope this helps!
NOTE: The above should be coupled with a long, slow ride as well to keep up your aerobic capacity. So each week you'd do 1 hill interval ride, one sustained power and one long ride. In between you can add recovery rides too (if you have the time).