I'm sure others will be along with more sage advice, but IME running and bike ones are slightly different mounts / requirememts.
I had a cheap one that loose signals from the heart strap irratingly often. Running ones on the bike are ok but you have to take your hands off the bars the see the readings – or strap it on the bars.
In the end I'm happiest with a garmin forerunner 305 that's slightly bulky for running but great on the bike with the optional bike mount (download routes, shadow laps, totally waterproof, crashproofs, cadence, heading….). In the 18 months I've had it there hasnt been one dropped signal and lasts 8+ hours on a charge etc.
If I had to look at a new one now I'd stick with Garmin.