I always think of it as the English word "thrives". I think the words share the same Old Norse root.
My translation was "She thrives in her work" which I think is pretty good but it wasn't accepted. I think it probably should be.
Anyway my point is that it's easy for an English speaker to remember that it needs a preposition if you think of it as thrives.
Late answer about why 'thrive' should not be an accepted answer here.
If we talk about people, 'thrive' in English means something like 'prosper' or 'develop well' or 'do well'. trivas in Swedish means 'to be comfortable (in a certain way)'. Those are different things, and though they often coincide, they don't necessarily. 'She thrives in her work' might be translated as Det går bra för henne på jobbet.
If we talk about plants, there's the word frodas which means pretty much the same as 'thrive', but that's only rarely used about people and doesn't fit in this context (cannot be used with 'med'). For things like economy, blomstra 'bloom', 'flower' can be used. E.g. 'thriving economy' = blomstrande ekonomi.
You can't use trivs in the command form, that doesn't make sense because there isn't enough 'control' in the meaning of the verb itself – you can decide to 'enjoy' something, but you can't really control whether or not you're going to 'trivas'.
I'd say Ha trevligt på helgen! or Hoppas du får trevligt!
"She enjoys with her work" Interesting. Luckily using common sense I didn't write that. What is the purpose of the 'med' here? Why cant she simply enjoy her work, instead of enjoying with her work, it sounds like she's enjoying something else, and she is with her work whom enjoys it too, in the way you'd say 'She enjoys the movie with him'.