Bridges started slowly and Martin Grant had to make a couple of early saves before Hythe took the lead on 13 minutes when a left wing cross was headed by Dean Grant.
Soon after, Tony Garrod moved in from the right and saw his shot cleared off the line via the post.
Martin Grant continued to be at his best as Hythe looked to increase their lead.
However, Bridges were much more in the game themselves and equalised in the 35th minute when Tim Cook volleyed home at the near post following a cross from Kieran Allen-Djilali.
Garrod shot over close on half-time as Bridges finished the first half well.
Bridges really took the game to Hythe in the second half and could easily have scored several times.
Garrod went close on several occasions and Allen-Djilali saw a free-kick cannon off the bar.
Hythe were very dangerous themselves and had some good chances in an end-to-end second half.
For Bridges, Martin Grant and Alex Rose were tremendous with everyone putting in a good shift and playing some good football.
This was the best performance for a long time and gave hope that they can now go on and win the next few games.
Bridges: M.Grant, Pierre, Rose, J.Grant (capt), Mobsby, Odofin, Sargent, Hall, Cook, Garrod, Allen-Djilali. Unused subs: Lansdale, Tait, Wilson, Touray, Fender
Aerotron Man of the Match: Martin Grant