As a guy that bikes more for the aerobic benefits than the hobby aspect, a heart rate monitor will allow you to develop a pace that's not only beneficial to burning fat, but will allow you to enjoy the sport.
I ride a flat path with crushed stone and mud. To hit a HR of 130, I roll out 4:30 miles. To average 4:15 miles, I'm in the 140s. To hit a a 4:00 mile, I'm high 140s to 150s.
When I'm just sightseeing, a 5:00 mile has me around 115bpm.
So just picking up the pace a few miles per hour completely changes the effectiveness of a bike workout. The only way to keep you honest is a HR monitor.
Here is a link to a recent ride. I did ride to and from the trail head, so you'll see some downhill and uphill times. Miles 5-19 are on the trail.
http://connect.garmin.com/activity/549457427
Sent from my iPad