The percentage of the total project effort that is used to produce the quotation varies greatly depending on the experience of the person preparing the quote with the type of task.
Typically I see people doing their first quotation coming in at around 15-20% of the actual hours, and about 60-70% of the "hard costs" for the final bill.
As a general rule, experienced quote writers will get within 50% (from 50-150% of actual cost) for about 50% of their projects. Nearly all of the mis-estimates for experienced writers are due to "scope creep" so the actual project gets larger, not because the original estimate was bad.
If you can get a signed SOW (Statement of Work) that says exactly what the project entails, you can bid with relative safety. If the customer can not commit to what they want before you write the proposal, then do not accept the job as anything other than time and materials. Trying to do a job without a formal definition of what is expected for a fixed cost will kill you and ruin your reputation with the customer.
If you get the SOW, then work up your proposal. Allow for the fact that your first few estimates will be off by nearly an order of magnitude and possibly more, so push the ceiling up as far as you think that it will go... For your first few jobs, there is no such thing as "too much headroom" in your bid!
Just FYI, a few years ago when I was an independant I tried to slack off my remaining jobs before joining the company I work through now. I found an alternative worker for each client that I felt would do a decent job, then raised my rates and estimates through the roof... This didn't work well, I actually had clients choose to work with me (even when I pleaded with them to reconsider) and had new clients come knocking before I bolted the door for good! When you develop a good reputation for being fair and thorough, it is practically impossible to price yourself out of a job!