Simple steps for E53.

Set to full heat and blower on max.
Loosen the bleed screw on the expansion tank and remove the cap.
Add coolant until there are no bubbles coming out at the bleed screw.
Tighten the bleed screw and put the cap back on.
Run engine until it reaches operating temp.
After coolant has cooled check level and adjust to float max mark.
While only a precaution I check the coolant level after having driven at operation temp a few times.

There is no specific amount of time it will take for coolant to be at cooled down. I don't add coolant until front of cylinder feels cool to touch.
No need to drive anywhere for bleeding process to be successful just let the engine idle.
At no time add fluid over the max. Amount of air in system varies. Much easier to add coolant after air is gone than extract coolant if you overfilled more than the displaced air.
If you have a leak at the expansion tank you replaced check your work and the new tank for defect.
Until you have completed the bleeding process properly ignore leaks from cap.
Unless you have overheated due to not bleeding it properly the first time, based on your circumstances, I wouldn't worry about a blown head gasket. However, easy to eliminate. Coolant should feel normal, be normal color and clarity

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas