When a shy and reserved guy asks a girl her plans for the weekend and says he is looking forward to spending some time off his office stuff does it mean he is asking her out on a date?

I would say he was probably trying to open up a conversation that leads to a date. If you say he is shy, then maybe he was rehearsing this question. I faced the same situation before and I told him that I have to work on other stuff and asked him what his plans are for the weekend and he never got back. So was his question about my plans intended to be casual, if it was casual he would reply. But since he didn't respond, does it mean he was embarassed that he asked this question in the first place? Maybe Just nervous. Do you like him? It is totally okay for a girl to ask a guy out as well. Why don't you ask him to hangout sometime. Maybe you can get a better idea of what he thinks.