I've been analysing the performance of search within e-commerce sites for a while.  I've found the need for a specific metric to assess performance here.  I've come up with something I call the "Search Index."  This is the number of searches as a ratio of retained visits.  For example, if you had 100 retained visits, and 10 searches, your Search Index would be 10 - you get 1 search for every 10 retained visits.  If you had 200 searches and 100 retained visits, your Search Index would be 0.5 - two searches for every retained visit.    This is just a quick number so you can factor overall traffic variations into changes in site search activity.  It's important to be clear that a Search Index of  10 does not say that 1 in 10 visitors or visits involved search, merely that there was 1 searches for every 10 retained visits.  Some visits will involve multiple searches.  It's just a quick way of comparing changes in traffic volume with changes in internal site search.
I use retained visits rather than total visits as people who bounced, by definition, could never have used search in the first place.  Search Index is about determining how people who entered the site are functioning.

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