midi over bluetooth for my musical instrument

I have a musical instrument I made (from Peter D.) that I use with an iPad/iphone. It sends the midi data out over the Tx line from the pro mini, to a midi connector. I then use Yamaha’s iOS midi adapter and plug it into the iPad. See photos…

What I’m wondering is, the possibility of replacing the midi cable with 2 bluetooth modems from Sparkfun:

It says it works just like a serial pipeline, so there shouldn’t be much to it? If I setup the bluetooh modems to send at 31250 baud rate, then would it work like this:
add one bluetooth modem to my instrument (call it the master)
It transmits to the other modem (the slave), which would have it’s tx connected to the Yahama midi adapter. Would I need any other hardware on the slave modem, just power?

If my instrument’s pro mini is what is establishing the midi baud rate (31250), maybe it doesn’t matter what the bluetooth link baud rate, as long as it’s at least that fast?

One more question: The Yamaha adapter for the iOS device has a 3 prong stereo jack (see photo), or 3 conductors, which is what midi is–the +5volt, the ground, and the signal. So, if my iOS device can source enough current for the bluetooth modem, would I just be able to connect those 3 to the bluetooth modem without anything else?

A lot of questions here. Any answers or insight will help. Thanks.