Bubbles into the the cooling system overflow tank are normal if the system is not completely full and working normally. If the radiator cap is good, the overflow line to the overflow tank is good, the pickup tube (if there is one) is there and there is coolant in the tank each heat cycle of the engine will draw coolant out of the overflow tank and back into the radiator as the engine cools.
As the engine warms the coolant expands and forces either coolant or air out of the top of the radiator and into the overflow tank. In the days of old there was no overflow tank, that excess went onto the ground (bad) and the radiator was never completely full when cold (owner's manuals used say the system was full when coolant was around an inch from the top). For a few minutes after you shut down the engine the coolant gets warmer and expands some more (more bubbles?). As the engine cools fluid (if the pickup tube is submerged in coolant) is drawn back into radiator.
So if there is no over heating and with each heat cycle there is less coolant in the overflow tank (indicating the system is working correctly) and you keep topping up the coolant in the tank, it will fix itself over some period of time.
You can speed it up by manually filling the radiator to the top each time the engine completely cools.