On my phone (android) I can have several bluetooth devices connected at a time. At least, I can sync my fitbit while streaming music to speakers and sending pictures to my computer, that sort of thing.
However, I concur with Oakleaf that a HR strap is the way to go. The newer ones aren't that uncomfortable, although I am glad to take it off the same way I'm glad to take off my bra at the end of the workout.
Definitely go with an older model for now. I bought my past computers on ebay. You could also try craigslist, or a lot of places like clever training and heart rate monitors usa have discount codes you can use.
2007 Trek 7.2 FX
2015 Felt F85X with Specialized Oura seat, Specialized Road Pro II handlebars, and Look Quartz pedals