I don't think you're overreacting at all, OP.
It's easy for people to say "Just talk to her" but she's obviously made the decision to use the bins, knowing that the tenant will then not have their own bins, and reckoned on avoiding paying for a regular trade waste collection at your inconvenience.
I wouldn't worry if it were just a little bit and it would be unused space that you wouldn't ever need yourself; but just taking the whole bin(s) and leaving you with no bin room at all is deliberate, selfish and certainly isn't coming from a respectful place.
If you ask her about it, I bet she'll just insist that they only use a little bit of space - but then keep on filling it all up just like before.
A lot of landlords are really bad at respecting their tenants' boundaries, and seem to think that, because they own the house/flat (for which you pay them rent), it's also their own home when it suits them.
When I was a student, 4 of us lived in a flat above a shop and the landlady (who ran the shop) and her staff also used our (only) bathrom/toilet.
It wouldn't have been quite so bad, except, after a few times of her waiting outside on our landing, giving us the evils, crossing her legs and doing the wee-wee dance whilst we had showers, she later told us that we couldn't have showers during shop opening hours - which extended several hours into the evening too, as she was a workaholic who would sometimes be in the shop (and thus potentially needing the toilet) until midnight or even later on a couple of occasions.
It got utterly intolerable when she also started letting customers use our bathroom as well. Once, one of us pushed the (slightly ajar) door, only to find a non-too-pleased man in there helping his little girl to use the toilet.
We also encountered people needlessly wandering into our own private areas as well - they may just have been too thick to understand "the toilet is right at the top of the stairs" or otherwise may have been pervs or wannabe thieves; who knew?
The landlady had a space at the back of the shop where she could easily have had a staff/customer toilet installed; she just didn't bother because them using our bathroom was only a problem for us, not for her.