B-1 is actually a business visa -- a tourist visa is B-2. I will assume you are talking about a tourist visa.
I don't have such experience -- but I know a number of Russians and Ukrainians who have applied, some successfully, some not. It is definitely a roll of the dice -- there is no way to be sure she will get a visa.
She has better chances to get a tourist visa if she:
* can prove that she owns a home in Russia
* can prove that she has a decent-paying career in Russia
* has child or children who will remain in Russia
* previously was granted a US visa, came to the US, and left the US when she was supposed to
The less she has of these, the poorer her prospects. As for "getting her" a visa, there is (as far as I know) nothing you can do to assist. As far as I understand it, application process is between her and the US State Department -- for a tourist visa, the State Department is not looking for citizens to sponsor or otherwise "vouch for" visa applicants (I'm not saying that vouching for a visitor is useless, but it may not carry any weight).
I agree with some of the feedback on your other topic. If you want to get to know her better, you might be lucky with the State Department, and she can come to visit you in the US. If you want to make a solid plan that doesn't depend on luck, go to her city, and/or spend some time together in countries that are easy for her to enter (for example, Ukraine or Turkey).
she doesn't have any of the above mentioned criteria. She's a poor traveler looking for adventure. Well, so am I. We found it in Laos. Then Thailand. She's still over there working at a bar for room and board. Tommorow she says she will talk to the US embassy in Bankok and see what she can do. Probably has to return to Russia and apply there. Sigh.. might be a lost cause. Plenty of American girls around, but everyone here probably agrees with me, they are just not the same. Thanks for the advice durak and bowhunter.
wildwest chances are she will not be able to get a Visa as they are very difficult for Russians to get. if you decide you want to be with her fiance visa is a simple process but she will needs police report from every place she has lived for more than six months. the police report will need to be done within six months of her interview at an American embassy provided you are American. I have experience in this type of visa.