You can buy the Garmin heart rate strap separately (you don't have to get the bundle with the Edge) and they pair just fine. Eventually the HR straps wear out/stop connecting as well (when that happens I get crazy HR readings -- like starting at 280, decreasing as I work harder) so I bout a separate Garmin heart rate strap at REI (I think about $75) and it paired easily with my Edge 800. I've also used the Wahoo bluetooh HR monitor successfully with both my Edge and my Garmin watch (FR 610).

I wash my Garmin strap weekly (just throw the strap, without the monitor part) in the wash and let it air dry when done and I've found that to extend the life before it goes wonky. I didn't like the chest straps at first, but now I don't even notice they're there. I'm pretty well endowed, and they fit right below the bottom band of my sports bras. Occasionally if things shift (mainly with running, never biking) the strap will shift on top of the bottom band of the bra and then it stops reading but that only ever happens with yoga type tops with the built in shelf bras and I don't use those to run or bike that often since they're not very supportive.