I never rode with one because i thought they were tacky looking under the bridle. Instead when we stop for breaks or whatever I would put the halter over their neck and slide the bridle on/off.
When putting bridle on I would put my arm under their cheek bone up over their forlock kinda thing and slide the bridle on over their head while the halter is around their neck. When putting halter on i would take the bridle down so the bit falls out of their mouth and put the headstall around their neck.. either way there is something on them all the time in case God forbid they were to try and take off. When on the trails depending on the horse I would ride in a rope halter, no need to even use a bridle. On horses that were not trained to ride in a rope halter i would put the halter/lead rope on the saddle horn when riding western.