Get first class and crossdressdress as a rich woman of that time
First class women had the best chances of survival.
First you need to getGet hold of a first class location and/or ticket.
IfEven if you happen to beare female, then you need to get conforming clothes, your 21st century wear needs to be recognized as 100% female in an emergency, you cannot risk it.
If you are male, you also need to shave and you need to do it as soon as possible.
Your best chance for obtaining the needed clothes is kidnapping or seducing a drunk passenger from the first class. In case you go for kidnapping, you can try going for a seasick first class female passenger.
If you get the chance to prepare for the journey, you go for Miss Edith Corse as to not interfere with the survivor list.