Yike, this will be a huge job if you get it, good luck.
Car parks normally sub-contract the work out to a property management company, if they use one why haven't they asked them, who usually cleans the premises?
I don't know anything about jet wash work, but the things you need to get the quote in are:- an idea of how long its going to take you, how many people and the time of day. I'm guessing its going to have to be cleaned at night when there isn't any traffic, you should be able to charge a premium for that.
You will have to dramatically cut your price to get the work, unless you are extremely lucky!!
So, how many square metres can you clean an hour, how much chemical cost and machinery cost. How many people, then add on your profit.
Hope someone else can help with the pigeon poo!! It is a hazard, so should go in a yellow waste sack, these are charged at about £4.00 per bag to dispose of. Wear gloves and possibly a mask. What will happen to the waste water? You might have to look into that too, with all the pigeon poo it can't go down a storm drain.
Should be a good earner, as its not everybodies 'cup of tea'.
Good luck.