Sure, but be prepared for a no for a myriad of reasons that are nothing to do with you at all: she has a partner, she's happy being single, she's got no time, she's contractually not allowed to date customers, she's not hetero, she's had bad experiences, she doesn't data strangers, etc.
But why not? "You seem such a lovely person. Can I invite you for a coffee soon (or whatever it is you plan)?" If she says 'no', at least a nice person got a compliment, which is always a win. And you get to know it's no big deal to basically communicate "you seem nice, and I like being with nice people" which is hardly taboo, is it?