Bill is a theatre director, which means he's Margo's boss, in a way, in addition to her boyfriend. The movie isn't concerned with Bill's professional life with Margo, only their private life. Which is good for us, because his private life is a lot more interesting than what's happening on stage.
Bill's devoted to the theater, but he's not a pretentious jerk about it, unlike some of the other characters. We like to think he's channeling Joseph L. Mankiewicz when he says to Eve:
BILL: The Theatuh, the Theatuh… what book of rules says the Theater exists only within some ugly buildings crowded into one square mile of New York City? Or London, Paris or Vienna? Listen, junior. And learn. Want to know what the Theater is? A flea circus. Also opera. Also rodeos, carnivals, ballets, Indian tribal dances, Punch and Judy, a one-man band: all Theater. Wherever there's magic and make-believe and an audience, there's Theater. Donald Duck, Ibsen, and The Lone Ranger, Sarah Bernhardt, Poodles Hanneford, Lunt and Fontanne, Betty Grable, Rex and Wild, and Eleanora Duse. You don't understand them all, you don't like them all, why should you? The Theater's for everybody—you included, but not exclusively - so don't approve or disapprove. It may not be your Theater, but it's Theater of somebody, somewhere.
First of all, props to Bill for dating a woman 8 years older than he. A very strong, outspoken, opinionated older woman who's way more famous than he is. In 1950. That counts for a lot in our book. Bill loves Margo, but she's afraid that he'll leave her for a younger woman. He's done nothing to make her suspicious; it's her insecurity talking. It frustrates him to be accused of something he'd never do.
One of the first times we see Bill, his love for Margo is evident. She's not wearing her wig and has tape around her hair; she has cold cream slathered on her face; she's described as looking "like a junk yard," but Bill's still gaga over her:
BILL: My wonderful junk yard. The mystery and dreams you find in a junk yard.
Never have junk yards seemed like such a compliment. Compared to a summer's day? Boring. Compare us to old tires and broken axles any day.
However, Margo lets her jealousy of Eve, specifically Eve's youth, get the better of her despite Bill's protests. When Eve takes over as Margo's understudy, Margo believes it's because Bill has the hots for her. He tries to convince her otherwise:
BILL: I love you. You're a beautiful and intelligent woman, a beautiful and intelligent woman and a great actress, a great actress at the peak of her career. You have every reason for happiness, every reason, but due to some strange, uncontrollable, unconscious drive you permit the slightest action of a kid, of a kid like Eve to turn you into a hysterical, screaming harpy! Now once and for all, stop it!
Bill has a point. Margo's worried about being seen as a hysterical screaming harpy, and her insecurity, as a result, turns her into a hysterical screaming harpy. Bill can't do anything about it; he decides to leave her.
After Eve's bravura performance as Margo's understudy, she decides to make her move for Bill. He rejects her advances in no uncertain (and very macho) terms:
BILL: I'm in love with Margo, hadn't you heard? […] Only thing, what I go after, I want to go after. I don't want it to come after me. Don't cry. Just score it as an incomplete forward pass.
Bill rushes back to Margo's side as soon as he sees Eve and Addison's nasty article about her—a "piece of filth," he calls it. He sets us up for Margo's surprising decision to abandon her career for him when he tells her:
BILL: Bill's here, baby. Everything's all right now.
Mr. Romantic breaks the news to his good friends about marrying Margo:
BILL: I'm going to propose the toast. Without wit. With all my heart. To Margo. To my bride-to-be.
MARGO: Glory Hallelujah.
Swoon! We imagine they lived happily ever after. As Karen says, "They'd die without each other."
Behind the Curtain
We know all about Bill's personal life, but not his professional one. Despite being a director, his role in the theater isn't discussed much. Eve, early on when she's still tricking us into thinking she's a decent human being, says Bill is "the best." Karen quips, "He'll agree with you." That's just good-natured chiding on Karen's part, though. Bill isn't cocky like that. He later says, "Geniuses don't need good luck. I do." A little bit of self-deprecation looks good on a man.
Now, just because Margo has to fret about acting and her love life and Bill doesn't, don't be confused into thinking this is a role reversal between the two, with the man's career being taken for granted while focusing on his romantic travails. No, the reason the movie doesn't focus on Bill's directorial career is because his career is guaranteed. Unlike Margo, who has to choose between a professional acting career and a private life as a wife, Bill never has to ask himself that question. He gets both.
Note to self: Jon Hamm as Bill in remake?