I've been doing freelance web design for a couple years now for guys in my town. I originally started charing by the hour, its way easier if your just starting out.
When you make a bid you are just multiplying your hourly rate by the amount of hours you expect the project to take. When I tried giving them a bid I usually GREATLY under estimated the time it would take to complete the project and ended up spending more time then I thought I would, and thus loosing money.
I suggest you charge by the hour, and LOG ALL YOUR TIME (Time you work, phone calls, in person meetings, all of it). If you decide to do bid, take the amount of hours you think it will take you, and multiply that by 1.5... That gives you some wiggle room.
As for how much you should charge... Its really what they are willing to pay. I charge $15/hr. The clients I took were paying $90/hr for a worse job. Since this is your first time I would recommend not charging more than $25/hr. As you build your portfolio and your experience you can start to charge more.