In my opinion, the fact that u didn't manage to meet up & she says she's usually very busy is def not a good start and is quite tricky to recover from that.
I think u went wrong with ur text as well and I'll explain:
1) "Let's meet up in the week" - shows indecisiveness. Tell her when u'r free on a weeknight and that she should join u for whatever you've planned. Come across as busy and like you have lots going on.
2) "so we can get to know each other better" - way too AFC
3) "let me know what times you're free" - you're too available here, like u said, be more assertive
I would rather have texted something like this:
Ciao *her name*, there's this really cool place in town where I'm heading tomorrow where *insert fun personal joke*, you should come join, will be laugh! P.s. One can never be too busy for a fun time, well that's if you can handle it...
You right in saying the language barrier makes it hard thou! I once was so relieved to get rid of this russian HB 9 just because I literally just couldn't speak to her + she was kinda cooked in the brain as well, haha! But Good luck anyhows!