Asking a girl on a date that I barely talked to

Hello guys! Since about 2 years I (M26) go almost everyday to have a Lunch with my father in a restaurant and I like the daughter of the owner of the same restaurant, she works over there. My father is very extroverted and he noticed that I like her and sometimes plays with her and calls her daghter in law (in my language is actuallya cute name) and she always laughs and seem like she likes me too, but the problem is that I'm very shy and she's also very shy, the most tha ti talked with her was to ask how she was and one time she had an accident and she was limping and I asked her what happenned and she took a long time to answer (it was a bit awkward) I think she took a long time to answer because she is very shy and wasn't expecting that I was asking her that. The thing is that I'm pretty sure we like eachother but we're too shy and she doesn't even know my name (at least I think that) but I know her name, so I wanted to ask for advices since I know eachother for a long time, almost never talk to eachother, how can I start to talk more with her and ask her on a date, since we're very shy and she's also working and I don't want to interfere with her work. Sorry for the long text and also if I made any grammatical error. Thank you in advance.