Letter of invitation

You want to do this with the right letter the first time.

Perhaps the US immigration or Poland has a special format, or perhaps it is as simple as including the following kind of paragraph in a very short, special purpose, letter to her.

"I'm inviting you to visit me in the US for __ weeks so that we can continue to learn more about each other.  I will be responsible for your airfare, room and boarding."  [you make the facts fit your situation]

I think you need to find out if US immigration or Poland wants anything further such as notarization of the letter, special form of mailing, how you are to demonstrate you have done the proper invitation letter, etc.

Also have them tell you anything additional you or she needs to know.  For example, information about the visa, passport, her documentation, maximum length of visit, etc.

Here is the type letter of invitation I wrote for my firends form Asia:

Dear Topik:
  It was very good to see you again and thank your family for being so nice and hospitable. We'd like to invite you to visit us in the USA when you get some free time. Hopefully you can ask for a couple weeks off from your employer. Don't worry about accomodations as we have a spare room and plenty of extra food. We'll hope to hear from you soon, so we can make reservations for your round trip flight. Just bring a little spending money for some gifts for your family and friends back home.

Sincerely,

Now with a female it may be different. If she is coming as a tourist, she'll need a letter of invitation from you, so THEY, the Embassy in Poland can "estimate-guess" if she has reasons to go home after her visit. They require economic ties like bank accounts with money, real estate. Then social ties like a family and really they mean husband and kids, but that would not apply to you, hopefully. Then professional ties, good job. A "good license" letter from her police dept. shows she is not a criminal.
I got a USA friend who got scammed twice into sending money to to ladies for passport, etc. Hopefully you have been to Poland and know everything about her and her family.

Now the way I wrote me letter had meanings:
1. The Embassy at the interview for the visa will ask how do you know this person in USA? My letter showed I'd had been there before AND my passport proved it and we had known each other a good while. And I knew their family.  If you and your lady are penpals, that is not a good answer for the visa interview.
2. ALL expenses are paid so they know my friend will not get here and need government help.
3. The letter shows that my friend is not coming here and does not know anyone.
4. It suggest that my friend ask off from his GOOD job, and housekeeper, say for a female, won't fly.

The best situation would be if she is still in college, that is a reason she won't try to stay beyond her visa. Now if she is coming on a financee visa, well, you got 90 days to marry or the plane to take her home will be waiting at the airport.
If she is out of school and has only been on her GOOD job for a few months, this is not good. I was told they like them to have been on a job they need to return home for, around 1.5-2.0 years, to show professional ties.
Would my friend who runs an internet cafe be given a visa? In Indonesia no, since he would gladly give up such a low type job to get to the USA.
My other friend got his visa and came for 2 weeks.

Now Poland and Asia are probably two different animals. Alot of Muslims in Asia and many hate Americans so the Embassy's are ultra careful.

I'm not trying to offend you or anything, but I got scammed by a Russian.
Do you know:
1. her physical address in Poland?
2. talked to her on the phone with a phone other than a cell phone on her end, like the phone in her house or parent's house?
3. Have you sent her a $10 bill as TEST to her home address and she has confirmed she got it? DON'T tell her you are sending it, let her get it, be surprised, and ask you why you sent it. $10 is not the point, the point is to test the mail to make sure it gets thru in case you want to send larger amounts, and that her home address is correct.
4. I've been told NEVER send anyone overseas money. Let them us their own for their passport and has your lady sent you a copy of her passport?
5. Will she pay for the visa ($125) out of her pocket and send you a copy of her visa?
Again, I'm not making accusations, etc. I'm telling you the checklist of things to do, if you have never met her in person.

P.S. if she has a beautiful sister or friend tell her I'm now available and looking if her sister or friend are looking too.