Hey Chris,
I'm going to address your concerns in-line as I think that's the best way for me to clear up any confusion here.
"My assumption is that organic ranking of my landing page will be effected by bounce rate. When a shopping campaign sends a user to my page and they bounce, Google will see that as a poor user experience with no engagement. This is caused by the Google shopping campaign choosing irrelevant keywords that I have no control over. Running a shopping campaign causes the analytics data to have significantly higher bounce rates and therefore I would think hurts organic ranking of the page."
Your organic rankings will NOT be affected. User engagement signals from AdWords will affect your AdWords quality scores, but under no circumstances will they affect your organic rankings. Google states this publicly, like this example, "Running a Google AdWords campaign does not help your SEO rankings, despite some myths and claims.". It does not hurt, it does not help. The data sets are completely separate. Yes, in your data you can see them combined if you wish, but Google Organic does not see your Paid Ad Engagement Metrics.
As far as control over your Google Shopping, while Google does sometimes trigger terms that are outside the norm, their matching is generally pretty good. I would encourage you to review the post I linked above and to read other articles about Google Shopping Structures. Your structure is everything for AdWords, but it's especially true for Google Shopping. If you're having trouble with targeting, especially after reviewing the search query report and adding negatives, something is wrong with your setup. Review some posts and see if you find anything that might prove valuable.
"So I am paying Google money to lower my rank because of their bad choice of keywords. Google shopping does not allow me to choose the keywords. And the only way to control this is to use negative keywords as you suggest. In my experience this is also not very effective."
I addressed this a bit above, but I think it's worth reiterating here, your paid ads are not lowering your organic rank under any circumstances. Even if they share a landing page, the paid ads will not affect your organic rankings.
"Here is one example. I have a product with the word "Oxy" in the name. Google shopping sent thousands of impressions for queries related to Oxycodone and Oxycotin drugs. My product is an immune support antioxidant supplement for DOGS! Regardless of negative keywords set with adwords support folks on the phone, they continued to send queries for all sorts of variations. Such as "oxycodone 10mg" "buy oxycodone" ad infinitum! Even setting negative keywords to "broad" didn't help. Eventually tapered off after setting many variations as negative keywords. Close to 50 variations.
So of course these clicks seeking oxycodone immediately bounce when they see it is a product for dogs. My question is does that ultimately hurt my organic ranking?"
This sounds extremely frustrating and I'm sorry to hear that you're having these issues. I'd encourage you to add "Oxycodone" & "Oxycotin" as negative phrase match terms. That should solve your negative targeting issue as described.
But even if these issues still continue to arise, rest assured that your organic rankings will not be affected.
Hope that helps! Let me know if I can be of further assistance.
Best regards,
Trenton