Ben would have gone out to investigate this dark Wonderland with or without Dean. He thought of himself as capable of fending for himself. But in the end Ben decided to let Dean have this one. After the memories and remembering their relationship, he wasn't eager to strain that connection. Besides it wasn't as if Dean said he couldn't go out, just that he wanted it to be with him. However, he was incredibly eager to venture outside.
When Dean mentioned inviting someone named Jo, who he didn't know at all, to check out their new surrounding environment Ben had decided to invite Tandy. Next to Dean, Tandy was really the only other person he kind of knew here.
Going out into Wonderland came with its own dress code apparently. It wasn't half bad. He still preferred his own clothes but the assortment of weapons was pretty cool.