Based on the information I believe you went to a preliminary hearing date. If you were in jail at the time and then later got out on bond by law...

Absolutely not!!! In fact if law enforcement is requesting a written statement it may mean they feel the oral confession may be invalid.

Can a lawyer respersent me in traffic court without me being there?

Yes. Usually an attorney will do what is called a "plea in abstencia." Many cases such as these are handled in this manner.