can you get a bid with a visible tattoo?

As long as it isn't vulgar, no one will care. Appearances don't matter a whole lot, character is what will get you a bid.

Allow me to elaborate further:
We have a few girls (i'd say three or four) who have visible tattoos in our chapter. Yes, if you show up to recruitment looking like you didn't try very hard, you won't do as well as some other girls. Look classy and put together. BUT since a tattoo is no indication of your academia, personality, fashion sense, leadership ability, community service, classiness, or overall ability to be a good sister, it won't cost you a bid. If you and the PNM next to you both look well put together and have similar high school activities, GPAs, your tattoo won't break or seal the deal, it'll come down to the conversations you have. At least, thats how majority of the houses are. (Obviously^^), there are a few who might try to write you off immediately based on looks, but that isn't a good indication of a good sisterhood anyway. If you still feel like your tattoo might get in the way of your chances, just try to make up for it by talking about what you have to offer. You can also ask your recruitment counselor when you get one for some advice.