Hi XXXXXXXXXX,
It isnt really possible to get air leaking into the system unless coolant is leaking out and the air is replacing it. If this were the case you would definitely have enough coolant loss to see either a puddle of coolant or steam escaping when it was hot. If you are able to bleed air out of the system and add more coolant it means that the coolant level still is not full and there is still air in the system. It is not uncommon for the bleeding procedure to take several times before all the air is out.
If you have any additional questions or need any more help, please just ask.
the first step is to make sure the coolant level is full and bled as best you can. then run the car until it gets hot then shut it off. Once it is off feel both the upper and lower radiator hoses for temperature. They should feel the same. Then run your hand over the entire surface of the radiator making sure it is also heated up evenly. If there is any disparity in the temp of the hoses or a cool area of the radiator then the system still has air in it.
If the temps all are good and even then you need to concentrate on looking for a leak. this leak could again be liquid or just steam. Once the system is bled there is no way for air to enter the system unless coolant is lost. The coolant has to go somewhere first. The source of the coolant loss will also be the source of the air intake. Get the car good and hot and check everything you can see thoroughly for any dripping or steam. Pinholes in radiators are common causes of this and can be tricky to find so make sure to inspect the radiator thoroughly, front and back.
Mechanic
20 years experience working on various types of vehicles