I have my site set up so that users can type in the name of a bar as the URI, and the links within my site are built the same way.
For example, instead of triadbarspecials.com/bars.php?id=234546456, I have the links set up as triadbarspecials.com/somebarname.
I’m using .htaccess to direct to the proper page. Is it best to use the first url above in my site’s links, or will search engine robots be able to handle the second url above?
Search engines will be able to handle the second variation perfectly fine. Actually, using such “speaking” URLs is usually referred to as “search engine friendly URLs”. This is due to the user seeing what’s behind some URL just by looking at the URL. In a similar way, a search engine can use the path as keywords.
Just ensure that most (or if possible; all) URLs are unique. The more pages serving the exact same content (the search engine usually won’t see a redirect to the same page) the worse this can be for your page. As long as the content is unique and/or different, this is perfectly fine (and as mentioned; more or less recommended).