Here is an idea. Try the homotopy coherent nerve. (This was originally introduced, sort of, by Boardman and Vogt in a topological context and was formulated for simplicially enriched categories (and please do not use `simplicial category' as it is ambiguous!) The H.c. nerve is related to the bisimplicial nerve by using the codiagonal of Artin and Mazur. (which has been mentioned in several of my answers!!!). Some details of the H.C. nerve as discussed in the nLab entry on that and there are links to elsewhere. A chatty discussion can be found in Kamps and Porter, (again that has been mentioned before :-))!
Hope this helps.