Super rude on her part, but it's also extremely intrusive, rude, and weird to walk up to a total stranger you've never even talked to and ask her to dinner solely because you've been sitting alone at the bar for three hours overhearing her complain to her friends about being single. I'm not saying it can't work if you're physically like an 8–10/10, but that's effectively all she has to go on besides this obviously weird thing you're doing.
"I'm not desperate" could totally be referring to what he did rather than how he looks. This is George Costanza shit.