I can't find any information on the Canon, but many HP printers support Bluetooth by just plugging in a perfectly standard USB Bluetooth adapter into their 'camera' USB port. (Works on both of my HPs.) Canon's website mentions 'setup via Bluetooth', but this appears to be referring to their general setup software, not the IP4300 specifically.
I would say go buy the cheapest Bluetooth USB adapter you can find, plug it in to the "PictBridge" port, and see if it works. If it doesn't, return the BT adapter.