Living in an apartment involves some give and take. I've had neighbors that enjoyed their stereo a bit too much, and one that had an entertainment system with the subwoofer sitting right on the floor. While having the pictures on your walls rattling is over the line, I always tried to keep in mind that it's only natural you're going to hear some sounds from your neighbors, especially ones you live under.
I would try having a friendly conversation with her to see if an understanding can be reached. If she sleeps during the day, it might be trickier. But if she's simply expecting to hear absolutely no noise from you, that's a bit presumptuous on her part. It may just be that she needs to understand what the sound is, first... and then also that it's something that would be once a day, three times a week, or whatever.. and last for 30-45 minutes or however long you use it.
If she knows when to expect it and how long, it may be easier for her to ignore it. I had a neighbor once that always had his stereo up on Fridays while he got ready to go out. It was a bit loud, but I knew it would be over in 20 minutes. So, I made that concession as just part of being in an apartment. Of course, hearing it at 2AM was another matter.......
If push comes to shove, you may have to get the landlord to come in and go downstairs while you use the trainer to see if they think its an unreasonable sound.