I think you should look at it from the perspective of the client. Clients want to make sure that they can feel secure in your ability to accomplish the task properly, and they want to feel like they will not be ripped off.

As someone who has hired contractors before, I can tell you what makes me feel comfortable. One is to hear specifics about how the contractor has experience with the specific technologies I use. If I am using Python/Django and the contractor mentions experience with that, then I know he or she read my specification and has the particular types of qualification that I need. I also like it when contractors have some open source work they can point to, since that gives me an example of their work and also makes me feel that they are active and interested in their field.

Not everyone on freelancing sites is choosing the cheapest bid. It might be worth it to you to give it a try even if you take a few less than ideal projects to begin with, just to build up a portfolio and a job history.

Also (and I know this view isn't super popular on HN), I like working with a new contractor on a fixed-price payment plan. If they are willing to do that, to me it indicates that they have confidence in their ability to complete the task promptly, and I don't risk that a bad contractor will drag the project out and cost me lots of money. Perhaps that would help you reassure clients that you are capable before they have had the chance to work with you, at least until you have a strong portfolio to demonstrate your skills. Good luck!