These are great posts and spell out clearly steps you should be taking.
People would much rather pay more and get great support, than pay a cut rate and get a bag of crap. Plus it has been my experience that clients that won't, or can't pay a decent rate will cause you the most problems.
Being part-time is not a problem, but companies do want to know that you are a serious business, otherwise they will fear being burned. The days of people trusting amateur design and programming are rapidly ending.
It's important to understand that websites are no longer static and they should be changing all of the time.
Being available when your client needs you is one of the most important lessons and competing in a bid situation is a reality for any public/governmental/non-profit, so you must have a good website yourself that showcases your talents. Goodluck.