You've got some serious questions you need to ask her. She would NOT have been admitted to Puerto Rico if she didn't have a valid US visa. Either she is lying to you, or she had a visa (and maybe still does) or it was revoked for some reason. You need to get to the REAL facts about that.
Secondly some tips and facts. First of all, even if she has property and steady employment, if she is young and good looking, it probably is not going to happen, especially if they know she has a BF in the states. Now, before you go off thinking "I'll just tell her not to say anything" think again. If you want to bring her here to the states and she denies you are her BF, then at the resident visa interview she will have to lie, and trust me, they will know. Don't do it. You will mess up any chance of getting a permanent visa later on. They keep records of this stuff and if they ask her questions regarding the relationship, and then see that she denied having a BF in the states, you will be denied because they can't trust anything she says. Whatever you do as far as the Embassy, DON'T LIE.
Thirdly, only about 1% of visa applicants are approved for tourist visas, mostly not young, good looking people, with BFs and family in the USA. Having family in the USA is NOT a plus here.
Writing a letter of invitation is not necessary, nor will it help any. Support is immaterial for a tourist visa, that only applies to resident visas.
All in all, I would say just forget it, unless you want to waste $100.
I am curious though, don't you want her to come here to the USA ASAP, or are you not that serious yet. If you plan to petition for her, don't file a fiance visa. Get married in the DR and file for a CR-1 visa. There are many problems with the fiance visa that you don't find out about until she gets here. They can't travel. The K1 visa is a ONE ENTRY visa. That means until her adjustment of status is complete, typically 3-6 months, she cannot go back or she will not be allowed back in the states. She also will not be able to work until she adjusts status, which again, can be 3-6 months or even longer in some cases. Then there is the adjustment of status fee. $1,010. Married folks don't have to put up with any of these hassles. If you have heard that the fiance visa is faster, think again. Here is what the Embassy has to say about this:
What is the difference between a CR1/IR1 and K3?
Which is better for my spouse and I?
Marriage-based petitions for spouses of United States Citizens fall under the immigrant visa categories of IR1 (for couples married for more than two years) and CR1 (for couples married for less than two years).
Once an I-130 petition for a spouse is approved, some US Citizen petitioners file a second petition (Form I-129F), so that their spouse may be considered in an additional visa category, K-3. A K-3 visa is a nonimmigrant visa which allows your spouse to travel to United States and apply through USCIS to become a Lawful Permanent Resident (LPR).
In the past, petitioners often applied for the K-3 visa class because these cases were processed more quickly. We are pleased to announce, however, that the Immigrant Visa Unit is scheduling IR1 and CR1 appointments as soon as all documents for these cases are received at the National Visa Center. As a result, there is little or no difference between the time it takes to receive an IR1/CR1 appointment and a K-3 appointment. If your spouse travels to the US with a K-3 visa, he or she will still need to apply for LPR status in the United States. If your spouse travels with an IR1/CR1 visa, on the other hand, he or she will become an LPR upon admittance to the US. By filing just the I-130 for the CR1/IR1 you save the filing fee for the K3 I-129F. In addition, you avoid the time, paperwork and fees associated with adjusting status in the US from K3 to LPR.
Please keep in mind that U.S. citizens filing an IR1/CR1 petition for a spouse must file separate I-130 petitions for any children immigrating to the US.
I would say the most puzzling part of this is the trips to Puerto Rico. This is not something that would be freely allowed without the proper visa. Have you seen the stamps where she was admitted? If not, I seriously doubt she got in to Puerto Rico, which IS the USA.
-Tim