On one hand, I agree with all the people who are telling you to "just do you" and order whatever you want. Peer pressure is dumb.
On the other hand, most fruity drinks are made to taste good first and get you buzzed second. I've tried all of the drinks of the day, and they're all tasty IMHO. If you find the alcohol taste in a Bahama Mama overwhelming, then there's probably no hope for you. Get a couple of drinks fruity drinks in you (it's perfectly fine to confess to the bartender than you're not a big fan of the alcohol burn and let him/her recommend something), and then from there you'll care less and less about the taste. But do be careful, the motion of the ship can exaggerate the effects of the alcohol and get you throwing it all back up faster than you think...
Have fun!