I definitely second the advice to ask for the letter of recommendation in person. It seems like you already have a rapport with this professor, especially if you've been coming in regularly for office hours, have done well in their class, etc.
If this is someone who is in the field that you want to go into for grad school, I would start off the convo with talking about your desire to go to grad school, how you're thinking of applying soon, if they had any words of wisdom or advice, and asking if they would write you a LOR. It really is that simple. Nothing to be embarrassed about!