I recently contacted a provider by email (there is no phone number in her profile or on her website) and, after some back and forth, we confirmed a date and time to meet. So far, so good. However, I just received an email asking for a deposit of about 50%, to be paid via Paypal. There was nothing about a deposit on her website or in her profile and she had not mentioned one while we were setting up the appointment. The unspoken assumption, for me at least, was that no deposit was necessary and, more importantly, that this was going to be an all cash transaction. I feel as if I have been misled. Am I justified in feeling this way and, if so, what should I do?

...she "all of a sudden" (it appears) wants one.  

I do not routinely collect deposits but there certain circumstances in which I would. However, I am always upfront with the gentleman before he books the appointment that I will be requiring a deposit. At that point, the ball is in his court whether or not he wants to proceed.  

Why not ask some of her reviewer's if she's trust worthy?

But it's a common scam.  Once she has your money and done nothing for it...  she can ignore you & move onto the next mark.    
BTW, PayPal is not friendly towards illegal activities & will freeze associated accounts.  Some have been a long time & never resolved.

I agree. A multi hour date, and your possible lack of reviews/ review site membership and other factors such as canceling dates with her in the past might be a valid reason for a deposit. However, the deposit request is often a scam.  
 
Are you giving us all the facts because it does not seem like it. If you are looking for a reason not to go thru with the date, you don't have to ask us. It's your money.

You provide very little info but you make it sound very sketchy to me. Even if she offers to drop the deposit requirement - as long as you promise cross your heart and hope to die not to no-show, of course - I'd be expecting more surprises. Upsell? Worse? Rob and run? (If she does have a Profile and good reviews, that's less likely.)  

I'll give you my paypal info, I think you should send *ME* the deposit.
I'll investigate for you, and send the money back when it's all clear.

The appointment is incall for 1 hour. I've never seen her before. I gave her contact info for 2 providers I've seen in the past. Based on her reviews, which are uniformly good, she's got her own place. I'm not sure what other information would be relevant.

I often require deposits, depending on the circumstances, but I make this clear on my website. Under my rates, I have a text box that says I require a $100 deposit if:
-You don't have references
-Our date will be longer than 4 hours
-You're a couple booking my time
-You need me to provide an incall space  

If it were me, I'd run away and find one of the perfectly wonderful women in this business who understand how it works.  

He should send ME the deposit instead. Just check out MY user name, I am obviously more trustworthy than you. lol