James Hammond came closest to breaking the deadlock for the hosts when his speculative effort from the halfway line rattled the woodwork.
The draw leaves the Hornets sixth in the table after seven games. Horsham are just a point adrift of place-above Enfield Town, and four behind second-placed Carshalton Athletic.
The Hornets turn their attentions to FA Cup matters this Saturday in a home third qualifying tie against Hanworth Villa.
See some of John Lines’ pictures from the game on this page and the ones linked, and read boss Dominic Di Paola’s thoughts in the West Sussex County Times, out on Thursday.
1. Horsham 0, Billericay Town 0 - the match in pictures
Action from Horsham's entertaining Isthmian Premier stalemate with Billericay Town Photo: John Lines
2. Horsham 0, Billericay Town 0 - the match in pictures
Action from Horsham's entertaining Isthmian Premier stalemate with Billericay Town Photo: John Lines
3. Horsham 0, Billericay Town 0 - the match in pictures
Action from Horsham's entertaining Isthmian Premier stalemate with Billericay Town Photo: John Lines
4. Horsham 0, Billericay Town 0 - the match in pictures
Action from Horsham's entertaining Isthmian Premier stalemate with Billericay Town Photo: John Lines