Here's how I would do it:
You stand on a bridge, looking at the world,
And, from a tower, nature-watchers are looking at you.
There's a bright moon beautifying your window
And you're beautifying other peoples' dreams.
Thanks for reminding me of Bian Zhilin--the last time I read him was several years ago, but I really enjoyed him then!
Overall, your translation was great!
Some specific corrections:
你的=your, not "you"
看风景的人=people appreciating nature, not "people appreciate nature"