I’ll just echo what a lot of others have already said: ride, ride, ride!
Also, be careful, but remember that there’s a happy medium to how much care you should take. Some of my best coolest rides were way longer than I’d planned on. I’d just go for it, because I’m sure you’ll surprise yourself with your capabilities. Just make sure to bring lots of water and food (Camelbaks are great for this, but I hate them and would much rather bring bottles and bags attached to the unicycle; that’s a whole different religious debate, and there are plenty on either side!). My theory is that you can go forever if you bring water and food, go just harder than you think you’d be able to hold onto for the duration of your ride, and take adequate rest. The way I’d say to be careful is to set up safety nets for yourself should you completely run out of gas, become injured, or become afflicted with something generally inconvenient and/or ride-ending. Bring lots of food/water/money/tools, maybe a map, phone, etc; maybe make sure there’s someone who can pick you up if the sky falls, but don’t let your caution prevent you from really doing what you don’t yet think you’re capable of.
If you can do 10 miles without a problem, try 20! It’s just two tens. If you can do 20 without feeling too phased, then try 60 on for size with some rest at each 20, plus whenever you feel like! It’s only three 20s! The worst that could possibly happen is that you don’t make it, and have to phone someone really really friendly for a ride. (And the worst that happens if no one’s available is that you spend the night at the roadside till the next morning, and somehow find your way home… how bad could that be in the scheme of things? Lots worse could happen in the daily course of things, I imagine. :)) You have to get way more tired than you think you do for that to happen, though. The longest I’d ever ridden on a bike before my first 100-mile bike ride was maybe 30 miles. I didn’t break any speed records on that 100 miler, but by golly I made it. After I’d done maybe 8 or 10 hundred-milers over five months or so, I tried a 205 mile ride (2006 Seattle to Portland), and though I was nice and dead by the end of the day, it worked out just great, and I finished!
I hear people talking about training to do a 50 mile or 100 mile ride, or what have you, always next month, but the truth is, you’ll never really “feel” ready. Just do it one random weekend, and you’ll either not make it (VERY improbable) or you’ll totally pwn it in that slowly-but-surely sort of way, and forever know you’re able to.
Also, perhaps playing a mind game with yourself will help. When I go on a long ride, I think to myself “ah, it’s just 7 hours, or 9 hours” or however long, and make sure I have nothing to do for the next 15 or so in case something happens. After all, many of us (especially me!) spend longer sitting in front of the computer wasting time without getting up to pee, so how bad could spending that time pedaling be? Sometimes acting to yourself like it’s no big deal may help to convince you that it really is no big deal; then you can just hit the road and have a great day spinning your cranks without caring about whether you “can” do it or not.
My advice is to just get up and do it, aware that you might fail, but ready to push through some discomfort (won’t call it “pain” yet) to do it. When I get up to go for a long ride, the awareness that I have the option of calling it quits serves both as piece of mind and as a motivator for me to not take advantage of that option. Give yourself the option of aborting your ride halfway through, and then start your 50 mile ride, and see what happens. It may sound stupid to think like that right now, but I am willing to bet you money you’d surprise yourself!