marring on a K1 visa, living in the Bahamas

[devilfish]

My girlfriend(Colombian) has been in the US for 3 months now on a tourist visa. I'm an American seeking advice what to do. We plan to live in the Bahamas ( I have a work permit) . We need to leave in 2 weeks

Should we get married in the Bahamas and apply for the K1 visa from there?

Can she travel to the US with her US tourist visa while the K1 is pending?

Any other options? I know I could get married in the US under her tourist visa, but it would take months until she has AP..

Thank you