Tips for women dealing with contractors

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My question pertains to how to avoid being ripped off by contractors. I had an experience recently where I asked for a bid on a project and it seemed pretty high. When I asked them for another bid with a couple of things changed, he wouldn't give it to me and instead wanted to know "what my budget was." 

At that point, I was kinda annoyed because he wouldn't give another bid and it felt like he was trying to rip me off. I ended up getting someone else to give me a bid on the project (with the changes I asked the original contractor ) and went with them. Turns out I saved quite a bit of money!! 

I've talked with a couple male friends and they've told me that women need to especially be careful dealing with contractors because "it's easier to rip off women."

I totally understand contractors need to make a profit and there's nothing wrong with that. But I also don't want to get ripped off either! This whole experience really demonstrated to me the importance of getting multiple bids and not disclosing a number to "my budget." 

What else can I do to make sure I'm not getting taken advantage of? I'd really love to hear from some female investors, but I know men can get ripped off, too!