All the 'burping' in the world won't get rid of the heater core air air if you have a tiny BHG. Been there, done that.:icon_evil
Now that my BHG has been repaired for 1 1/2 yrs, when ever I have the coolant out and refill, I don't have the gurgle sound for more than a few days.
Here is how (thanks to a post on SF a couple of years ago):
Remove the thermostat, cut the little dangly thing off, and drill the hole out to 4mm. Re-install the thermostat (use a tiny bit of silicone gasket sealer on the rubber gasket to prevent leaks).
Start car and let idle. Fill system back up, adding coolant as needed when thermostat opens. Let engine get fully warm until it want to push some coolant out the radiator. Install a known good cap ($6, new). Fill overflow bottle 1/2 way. Add more coolant to bottle if 'low coolant' light comes on.
Air will now be able to more easily purge out thru that 4mm hole. Life will be good.
If you continue (as mine did before the BHG repair) to hear gurgle, then you will need to fix the BHG.:nono: