I'm a 35-year-old woman, who was married to a man when I was young, in my home country. We had one child together, soon after which he and I divorced. A lot of changes have happened in my life since then: I've come out as a lesbian and fallen in love with a U.S. citizen woman. I'm thrilled to hear that, if we got married, I might be allowed to apply for a U.S. green card and join her in the United States. But isn't it going to be hard to prove that our marriage is real given my previous marriage to a man?
You're not the only one to have asked this question, based on the understandable concern with proving that your marriage is the real, "bona fide" thing, not a sham or fraud to get the noncitizen a U.S. green card (lawful permanent residence). However, unless U.S. immigration authorities have been living under a rock for the last few hundred years, they will no doubt realize that some people are bisexual, or change sexual orientations during their lifetime, or try to fit themselves into a role that society expects of them by getting married despite their sexual orientation, and so on.
That said, the immigration decisionmakers will certainly find out about your previous marriage. The question is raised many times in the paperwork to apply for a U.S. green card. You will, for example, need to supply your divorce certificate. And they are likely to take it into account in determining whether they believe your current marriage is real as opposed to, perhaps, an arrangement between good friends.
You didn't describe exactly why you married your ex-husband or how you regarded your sexual orientation at that time. Whatever the facts of the matter, however, you'll want to be up front in describing and explaining them to the U.S. immigration authorities (in your case, most likely a U.S. consular officer).
You might, for instance, consider getting a statement from a therapist, marriage counselor, or lawyer whom you met with during the divorce, if part of the reason for it was your sexual orientation and you spoke about that with them. (If you're on good terms with your ex-husband, perhaps he might even supply an affidavit on your behalf!)
It will also be important to supply the same types of evidence that every other married couple does in proving the bona fides of their marriage: wedding pictures, copies of letters, emails, or phone bills evidencing your correspondence, hotel bills from your honeymoon or other trips taken together, evidence of joint bank accounts, credit cards, and other financial holdings, and so forth.
For more guidance on the relevant rules and procedures, see Marriage-Based Visas and Green Cards.