I think a 60 miler in your condition is not that big a deal. I just started riding last year (even though I'm in fairly good shape) and ended up doing my first century last fall after only about 600 miles on the bike total. This year I've been able to ride about the same amount but I don't ride nearly as often as I'd like to. But as long as you are in decent shape, you should be fine. The most I rode before my century was about 55 miles...

Like anything else, if you track it, it will improve. So take note of what, how far, how fast, etc. And you should be fine...