@jamesandrew,
Don't make it dinner. Make it coffee or a soda.
"Do you want to get a coffee after work?"
That's your line. Simple. She might tell you she's not allowed to date residents or is afraid for her job, or has a boyfriend (or girlfriend) already. Please respect that.
She might tell you, not tonight, how about tomorrow (or some other date)? Then great! Or, she'll say yes.