Ride more, at the speeds you want to be riding. Make a genuine effort to go faster. If you're going out every day doing a couple of miles at 11mph, your body will be more than content to repeat that every subsequent day. The road to getting faster sucks, because it's not comfortable.
Don't look at training plans, don't overthink it. At least once a week, go out and ride hard. Harder than you feel like you want to or should. I've only been riding for 4 years now, and I started off with no preconceptions. I just went out and hammered it. I'd ride on Monday and not be able to ride again until Thursday-- not because of time restrictions, but because I was horribly out of shape and physically couldn't do it. Then I was up to every other day, then stringing days together, and now I ride at least 180 miles every week. Speed is a byproduct of conditioning. Ride more, lose weight, get faster, repeat.
Oh, and the bike matters very little, unless it fits you poorly. I have 30,000 miles on cyclocross frames with tires 32mm or wider, and my global average speed over those miles-- including all the time spent off-road climbing hills-- is 15.8mph.
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