I think my tattoo artist is really cool, and I'd like to be their friend (platonic). Is it possible?

Sounds kind of odd...like it would be a weird situation. I mean, what do you do, say, "Let's be friends" ? I suppose friendship could work out but how to approach it without seeming odd...difficult. And to be honest, how do you know she would be a worthwhile friend? People usually make friends with people they have things in common with.

You drop off some nice lunch and a drink, without sitting down in, as a thank you gift and friendship gesture, and say 'I figured you are probably too busy to get some lunch, so anytime you need something, I put my number on a card in the bag.'
I can't think of any other way. Keep in mind that a self employed person is not someone who generally hangs out. I would guess that your odds are low.

Thanks for the input, @odinn7 and @joypulv. They asked to stay in touch, though not sure if they are just trying to build repeat business, or if they actually dig me as a person, you know.

All you can do is take her at her word that she wants to see your art. If it was just a pleasantry, she will say not this time, and say it in a way that closes the door for the future. But what's the harm in asking? Yes, invite her to a show. But I still like the idea of dropping off some food and a note, and your number, with maybe a photo or two of your art, to keep it clear that it's about shared talent.

You don't have to push hard or be obsessed with a friendship, it will happen naturally, but you sound like you want to gain a friendship to see if there is more there. That's a different story, as just a friendship you already seem to have, and what you want is a date. Ask for it.

I know you said just platonic, but I don't think you have to work that hard for just a platonic friendship, it will develop on it's own. You don't have to make elaborate plans to bridge the gaps, so relax, and don't get so carried away. That is of course unless deep down you DO want more than a friendship.

I have dozens of friends, when I owned my business. Some of them clients, and others not. Why could you not be their friend? You can start by chatting online with them perhaps. Most tattoo places have people that hang around all the time, and share interest in tattoos

thanks guys