Drove V8 540i with expansion cap completely loose!

[Mclaren]

a week ago around 8am before heading to work i was doing a routine atf, oil and coolant check on my 1997 540i with 49,000 miles on it. i got an urgent call from the office and i simply dashed to close up my apartment, closed the bonnet and drove 7 miles to my office and whilst parking i noticed fumes coming under the bonnet and upon opening engine coolant was boiling out of the expansion tank. so i closed and tightened the cap.....went about handling my office stuff and after three hours filled the expansion tank with 3 bottles of tap water until the floater got to kalt. drove the car home and no issues.

Following morning i warm up the car and coolant boils over again and so i drove another car to office and left my 540. was on the internet googling that day and therein found the cold and hot engine solutions to removing airlocks. The boiling over stopped and have done the bleeding thrice with the bleeder next to the expansion tank. I cant seem to find the thermostat bleeder and dont even know if my v8 has one but some columns have said just that one next to the expansion tank is ok.

Now the dreaded 'check coolant level" has come up after driving 7 miles yesterday. gave it a bleed while hot after getting home. this morning floater was 2 inches above kalt (cold)limit and i bled both cold and hot engine methods. drove the car 20 miles before the "check coolant came in" each time dissappearing with corner arrows and coming on after switching off engine. Check 5 hours later and floater still above 2 inched above kalt. I am about to travel 800 miles in a week and i dont want the temperature gauge going red or something horrid happening. Many horror stories on the 540i but have had zero issues until now and which was pure carelessness. What is my problem do you think?