Presuming you have "done video" before, and presuming you have the qualifications to do the job, you should know that there is a definite difference between a private/public client and any government work.
First of all, almost all govt. work is given out on a bidding process. This is always true for federal work and most state work. You will know if this project is subject to closed bidding simply by the fact that you will have been given a fact sheet on the bid proposal - what it requires, what is involved, etc. If you carefully analyze what is asked and price your services accordingly, you will be underbid. That's because most government contractors know that they can increase the real bill by all sorts of reasons. Bid low, bill high.
IF you're looking to get a no-bid contract because it's not big enough or important enough to warrant bidding, then you're home free. Same holds true if the winner of the contract is not necessarily the lowest bidder, but "based upon experience, etc." This is really, really complicated on the federal level, but locally . . . it depends.
There are really too many unkown factors in your post to give you a better answer. What's the scope of the project, for example? Who are you up against? You MUST have some idea of what has been budjeted for the job. If $5000 has been allocated, you certainly don't want to bid/charge $500. And vice versa. This could easily be a $25-50k job if you're producing a national commercial.
Need more info.
Phil