Dudley wed Amy Robsart (sp?) in the middle of 1550. He was not quite 18 and she was the same age. Elizabeth was a year younger. His father was an advisor to Edward VI, but Robert was a younger son, therefore NOT a suitable candidate for the daughter of the late king (even if she was a bastard). By the time Robert and Elizabeth became close, he was married and had spent time in the tower for his father's treason in placing Jane Grey on the throne. His wife died under questionable circumstances. (And he was suspected of engineering it.) This suspicion alone precluded her from wedding him without loss of prestige (and possibly the crown).
Elizabeth could have wed any number of foreign princes (the marriage contract would preclude them, like sister Mary's husband, from exercising power within England), she wasn't interested in marrying, she was interested in power and the attention it brought her (a mix of both parents, there). (She might have preferred girls for all I know, or the rumors that she equated marriage with death because of her mother (and Jane Seymour's death in childbirth) and Catherine Howard may be true.)