Anytime you do strenuous exercise that pushes your body, you should give yourself at least 24 hours to heal & recover. I'd suggest 2-3x a week until you're comfortable. Then you could go every day, if you want to.
12 miles on a relatively flat path isn't pushing too hard (as long as you're not pedaling all out), but you should still skip a day until you're in better shape. Pushing your body too hard too early can cause injuries.
Make sure you drink plenty of water. Maintain the bike properly so that it's as efficient as possible.
As you get better, you should see your time to complete the path getting shorter. My wife rides once a week for exercise & takes about 1.5 hours to do 12 miles (8-10mph with breaks every 5-6 miles). I commute every day & do 15 miles in 50-60 minutes with quite a few hills. I would never expect my wife to keep up with me, so I let her set the pace on that one day a week.
Go at your own pace & enjoy the ride.