Embarrassed about money

Hi.  I sent a proposal to a potential client and I am feeling regret that I proposed a solution that costs “so much” – the thing is, I broke down the project into tasks and phases and estimated how long I think each would take.  But at my hourly rate, I think it’s too much and wanted to shave off time from my estimates because I am also thinking Potential Client won’t go for it.  Help!

C: Website project estimated at $x
T: That’s too much.
F: embarrassed
A: Cringe when I see she’s viewed it.  Shave off time from my estimate.  Believe she’s not going to go for it.
R: I don’t value my own work?