The RCD310 doesn't have any built in bluetooth receiver but it can use a separate one. This could either be a module under the seat or the "Touch Phone Kit" which will consist of a touch screen thingy attached the top of the dashboard. Do you know which one you have?
If it's the TPK, which I had, it's utter sh!te and I recommend getting rid of it from your dash. It doesn't support bluetooth audio, even though you can control your phone through it and even thought the RCD310 has a bluetooth option in the menu.
What I did was get an RNS315 off eBay which has bluetooth built in. But what you can do now (and I'm about to do it myself) is get an RCD330 instead. It's a plug and play replacement and has built in bluetooth as well as Apple Carplay and Android Auto. Make sure you do some research and get the right one because they don't all support Apple and Android. Once you install that you can get rid of any other bluetooth modules you might have in your car.