Brake bleeding doesn't really "improve" braking performance in the way that you think it does. Bleeding just removes air bubbles. And, unless you have a LOT of air bubbles in the system, the main difference after a bleed is "spongey feel" beforehand, and "firm, direct feel" afterwards.
The suggestion to get bigger rotors is good. Just do the research to make sure your fork can fit a larger size. Nowadays almost all forks fit a 200mm front rotor, but I'm not sure about a 2010 fork. If you can, I'd go at least 200mm front, 180mm rear.
Also, not sure what fmendes is mentioning, but typically, when you swap pads, the power actually improves after "bedding in". Basically this means do some test runs with the pads. Go up to a decent pace, then give it a good medium pressure brake pressure until close to stopping, and do that 10-20 times.
If you're looking to buy all new brakes, I found
THIS article really useful.
In that article, it talks about how important bedding in the brakes is to the brake performance.
4. Bedding in is everything
Bedding in your brake pads makes a huge difference to their performance. Initial repeated decelerations leaves a residue of pad material on the disc, permitting maximum friction and performance. On the dyno the brakes were bedded in with 20 cycles of 1 second pulls from 15 km/h, then 20 cycles of 2 second pulls from 15 km/h, repeated twice. During this process we saw the braking torque increase around 60% from the first pull to the last pull.
I recently grabbed a pair of TRP Quadiems from WorldWideCyclery for $205. They're currently listed at $237, but they have coupons/discounts pretty regularly.
They are functionally identical to the Quadiem G-specs in the link above, which usually sell for $400 per set.
Other good options, are Shimano SLX/XT, or the new Shimano MT520. The SLX sell for $75-90ish per side (front/rear), while the MT520's tend to go for ~$95-100. I went with the TRP because they are effectively high end brakes, for middle of the road brake price, and I've been really satisfied with them.
Good luck, and welcome to the party

. I only started biking last year, and I'm loving it.