I wonder…it probably wouldn’t have occurred to me if I actually grew up in those times, but since I have zero desire for pregnancy or children but wouldn’t have minded being married, maybe I could have sought out a gay male friend and made an “arrangement” with him–we get married, he gets to discreetly visit his boyfriend(s) as he likes as long as he’s discreet, but has to play the role of husband (including providing financial support) for me while I provide him with a “respectable wife”. We would be good friends but no hanky-panky, so no pregnancy. And I get to work if I want to/can find a job I like. Win-win! 
You could live with a sibling, or “take care of your parents”, but yes, a single woman who was not a widow living alone was unusual.
Almost certainly a draftsman. I started out making maps and plats, and am now in GIS. Just wouldn’t morph into the GIS job.
I’m a baker. I imagine I could use the same skills but the equipment would be different.
Probably a teacher. Possibly the spinster who lives with her parents and takes care of them. If the gods were kind, I might have ended up as some sort of writer.
Ignoring the difficulties associated with race during either time period, I assume I could have been a paralegal or some sort of legal assistant as I am now. If I have to account for race, I really couldn’t guess.
1954 Pilot
1904 Sailor.
1954, librarian. It’s what I have my degree in and would be now if the internet hadn’t happened and shifted my career into Web site management.
1904, perhaps still a librarian, or else a genteel, impoverished spinster-lady.
I think I could stick with my interests and training.
These are assuming it’s me, dragged back in time kicking and screaming.
1954 - library lady/patron of the arts - marry well and use wealth and connections to guilt people into supporting a community library. Probably get lynched for supporting desegregation and letting black people and communists use the facilities.
1904 - Seamstress as my paying job, and theatrical costumer to stay sane. Probably marry a fellow theatre person, preferably a tailor, and subsist on the clients who found our scandalous second jobs exciting rather than trashy.
1954: mathematician
1904: mathematician
1854: mathematician
1804: mathematician
…
0004: mathematician
…
505 BC: mathematician
Of course, there were long periods where it would have been in Babylonia, China, India, or Arabia.
Well, it’s not my career, but I can operate, maintain and repair a Linotype. That would have just about guaranteed work in both 1954 and 1904.
I started my undergraduate degree in physics and am now a professor though not of physics. I think if 1954 or 1904 I’d have stayed in physics since my field didn’t really exist then.
Either date, I would be a commercial artist or advertising copy writer.
I’m retired, but before I retired I was a computer systems analyst. Not a lot of call for those in 1954 or 1904. I thought of becoming a lawyer or a teacher before getting into computers, so probably one of those fields.
Hari Seldon, what was state of the art math in 505 BC? Would you have been a Mathematician or an Engineer?
Lawyer. So yay!
I’d have been in a smaller pot of university graduates, so I’d have either been able to stay on as a post-graduate or maybe got some government job.
Maybe teaching if I could make proper use of the old school tie.
My degree is in Aero Engineering, so I probably would have been employable in 1954, but not so much in 1904. Altho, I’ve worked as a mechanical engineer also, and if I wasn’t female, I could probably have worked in that field in '04. Chances are, tho, I’d have been a housewife and mother in both scenarios, because that’s what girls became, for the most part. In fact, that’s what my mother expected for me and she never understood what I did for a living for all those years…
First, my apologies for not being more specific: to me, “a writing job” isn’t the same as “being a writer.” When I said “a writing job” I meant a job similar to my own careers: proposal and technical writing, which are both historically male professions. In 1954 there were certainly many, many more men in those jobs than women.
Second, no one is saying that there weren’t any women writers in 1954. I said “quite difficult.” There are many best-selling female writers in this era, too: are you saying that making a living as a writer isn’t difficult? Or that it wasn’t harder (not impossible!) for women to be successful as writers 60 years ago?
I was trained as an electrician and later on did facilities management. I’m guessing I would have been employable as either in both years.