I'll try to be explicit:
met a girl on a train, talked all night, she seemed to be interested, got her FB, found out from photos she has a BF, messaged afterwards (very formal, it took her 1-2 days to answer without any follow-up questions. Pure politeness), last message did not answer at all, 1 month passed, came back to the town where she is living, sent an FB message to ask her to hang out with me in a very Beta manner (actually all my messages were Beta AF).
No answer.

Not considering the fact that there are googolplex of women around and I am just an infected beast, how, if at all, can I turn this train around?

Thanks