Elizabeth's main object was Elizabeth and her mantra the Queen song "Keep Yourself Alive" - this colored all her entire life. And even if there had been witnesses to the fall that killed Amy Dudley, there would have been the degrading her royal estate with the "Master of the Horse" rumors along with rumors that the witnesses were paid to testify as they did.
As I've pointed out on other threads, marriage for "love" is a recent idea. Before then, marriages were limited by social class, family needs, country requirements, religion. Mores of the times determined who one could and could respectably be introduced to - very critical for young women wanting a suitable marriage, women's reputations could be irredeemably ruined by rumor, being seen in the wrong company, or completely accidental situation that would today be only embarrassing.
The above applied triply to Elizabeth I. The fact that she learned early to "think like a man" may have saved the concept of a woman ruler (especially after Mary) for England. So, unless she weds the Duke of Kalamazoo or the second son of the King of Narnia (both with a marriage contract stipulation that they won't become King if she takes the throne), she'd better off not wedding as OTL.
If Mary had been as clear thinking and calculating as her younger sister, she'd have wed Liz off, send her to live with her husband (who will be English and not a Duke), get Parliament to pass another succession law that allows Queen Mary to select her heir and probably leave the throne to Mary, Queen of Scots - a fellow Catholic. While Elizabeth is English, there is still a bad taste in many's mouth about the circumstances of her mother's marriage and most view her as a bastard; by wedding her to a Marquis or Earl and making NO provision in Elizabeth's marriage contract about inheriting the throne, Mary has ensured enough in-fighting to allow Mary a chance to establish herself. (And, hopefully, will bring her down well before her death to present her as heiress.) Maybe not......