Can't use all caps in Subject lines, so I used *s instead of writing BAD IDEA!!  
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Unless you know who you are dealing with very, very well, do NOT leave a paper trail with CC or other personal payments.  
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As far as traveling with cash is concerned, I guess there are 2 issues:  
(1) your feeling of personal security
(2) explaining to TSA or others why you're carrying so much cash.  
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For (1), look into banking arrangements so you can get cash upon your arrival from a branch of your own bank or a corresponding bank.
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For (2), people have posted plenty of legit reasons to be carrying cash.  
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Cash is King.

Definitely do not pay via credit card. I can tell you that there are some of these women out there who will blackmail you. They are relentless!

But I have gotten deposits by PayPal-Amazon and other payment processing sites.

I'm afraid that with a debit card a client can call his bank and do a charge back or cancel the payment And I won't get paid for my services, I only accept cash.

If the provider is reputable and has Been in business in your city for a while , you shouldnt be too worried about her stealing your money just to ruin her reputation and mess up her business.