You betcha! I'm the same weight, although a bit younger (30's). I believe that, barring serious medical limitations, you can accomplish whatever you set your mind to. It's all about baby steps. The good news about cycling is that your weight doesn't affect you as much as running or other high impact sports would. There's less stress on the joints.
I road a lot as a teenager but, until last summer, hadn't been on a bike for over 10 years. I became determined to rehabituate myself and have been fairly successful. A 10 mile ride isn't the big deal it used to be. I do have a couple pieces of advice.
First, get proper bike shorts and leave the underwear at home. Us large ladies have more flesh to rub together and it helps to have small or no seems to rub against us. I get seriously chaffed if I ride more than 10 miles in regular cotton exercise shorts. I also recommend paying attention to your knees. Concentrate on keeping them above the ankles. It will feel like you are knock-kneed but with our larger thighs, we have a tendancy to point our knees too far outwards which causes balance problems and can cause knee pain.
Lastly, even if you are riding to lose weight, if you ride longer than an hour, bring snacks along and eat frequently during the ride. I'll never forget the first time I hit 15 miles on an empty stomach. I felt like I was going to fall off my bike.
Happy riding!