look for a steward. if you don't know who one of your shop stewards are, look for people who wear teamsters shirts to work and ask them if they know. usually they will. your sup will not know. your sup definitely does not want you to join the union so he will try to deny its extisence.
anyway, get your card. get in it. i know you might think it sucks to pay dues but when you need the union's help when you get wrongfully disciplined or even fired, you cant say "ok i'm ready to sign up now". doesnt work like that. find your steward my friend. and be SURE to let him know if your sup or anyone else in management has anything negative to say about the union AT ALL because that is illegal. when i started at ups, my trainer tried to tell our training class that they will come up to you and try to get you to sign up so they can take money from your paycheck every week. that little comment did not go unpunished.