When you say you have "bounce issues", just know that I've heard that 1,000 times, and about 850 times, they imagined it was an issue.
Bounce is just like my mom's pretend friend, old bad Dorothy, she got blamed for most things, cuz the blaming was so easy.
Bounce is a relative measure, and it is very misunderstood and misinterpreted.
Sometimes a bounce event indicates you immediately and completely fulfilled the visitor's quest for info... so a high Bounce rate, and a following lack of further searches on that search issue, would be a good thing.
Generally, they are crawling and measuring.
#1 is the game you are playing (2,3,4,5 must be good, regardless of relevancy).
In other words, if 2-5 are tanked up, they will wreck all of your keywords' QS.
And, 2-5, most often, are site-wide issues, not page or search specific.
The game is, how hard to push...
If you shotgun and aim wide, the costs for the incremental traffic (as relevancy decreases) gets far more expensive per click, the less relevant shots are costly.
If you rifle and aim narrow, the CPC stays low, and QS is your pal.
G achieves this by pushing down your QS when you shotgun it.
If your landing page lists 12 breeds of live rabbits for sale... and you bid on "apology gift"... it's buckshot baby!