Before I go into whether I believe bounce rates affect your rankings on the search engines let me give a brief explanation about what a bounce rate is. For people who are familiar with this you can skip the next paragraph if you wish.
What is Bounce Rate
A bounce rate is when someone visits your website but only visits one page. In software such as Google Analytics this is shown as a percentage. So a simple example would be if you had 2 visits and had a 50% bounce rate then 1 person has visited just 1 page on your site and another person has visited at least 2 pages.
Does Bounce Rate Affect Rankings?
So to the big question of whether bounce rates affect your rankings on search engines.
There are arguments for both yes it does and no it can't possibly.
No it shouldn't because if someone typed in a very specific search term, clicked on your website, read the whole article or picked up the telephone and enquired about your company but never visited another page on your site this would be classed as a bounce. Which doesn't seem fair.
Yes because low bounce rates mean or are perceived to show that people love your website.
I have got experience of a site where the bounce rate was very low, less than 10% until one day when the bounce rate increased to around 80%. This wasn't picked up initially and even when it was it took some time to sort out the issue. Rankings around this time slipped but nothing drastic just a couple of positions. Over the period of a couple of months it became apparent that visits to the site were slowly fading but again nothing major.
Once the issue with bounce rates was fixed rankings slowly started to improve as obviously did the visits to the site.
As I am sure you will be aware with rankings there are so many factors that are looked at so it is possible that something else was going on but as far as we could tell there was nothing significant. According to Moz there were no major algorithm updates during this time, there was no change at all to the website itself however there were ongoing marketing activities albeit at the same rate before and after the bounce rate changes.
So something tells me that Google does somehow use bounce rate as a ranking factor. It is possible that they compare your bounce rate with other sites in your sector or compare bounce rates by keyword.
I have a feeling that you won't be penalised for a high bounce rate but could be rewarded for having a low one.