The best replacement for bridle is hackamore.

The best alternatives to bridle are rated as following:
★★★★★  hackamore
★★★★★  halter
★★★★  brank
★★  pelham
★★  headstall
★★  side pull
★★  latigo
★  saddle
★  traveller
★  western bridle
★  bridal
★  depower
★  dr cook bitless bridle
★  bosal
  horse size bridle
  bitless bridle
  english bridle
  figure 8 bridle

Your alternative for bridle is not listed? Suggest!
Speaking about bridle, one probably shouldn't forget about bit.

Other search terms related to bridle and their ratings are:
★★★★★ bit
★★ snaffle bit
You have in mind a companion for bridle and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of bridle in all years. Click on graph for more.
bridle
hackamore
halter