node access by related fields
I can use the exposed filter to manually select any matching nodes,
  but do not know how to automatically filter the queried RideShares to
  the current user's data in other bundle/content types. For example,
  whether the current user has entered a Flight into where the
  destination airpor catches one of the existing RideShares.


Views is a simple query builder. Typically this would be SQL like Select * From RideShares Where city = 'denver'. Your question cannot be expressed in single SQL expression you would need JOINs in SQL of PHP and multiple queries to arrive at an answer.

Your talking about relating a set of results with additional logic or data-sources.

This can be done in Drupal using a combination of Views Relationships perhaps Attachment Views to build results you want. 

For example I might create a Nodequeue of uids that are users on the same flights as me and examine a View result that uses the Nodequeue as a Filter against the current user to see if that logic produces any results.

You could then place many view blocks on a single page that acts as a search results page. Each block can be a View with many view-attachments, etc.