Few people use Bridge for this, so you won't find plugins or scripts. You're going to have to learn something.
The new Lr galleries are mobile friendly, so you could generate galleries as you do, but using Lr. If you get LR/PS by subscribing, there is an alternative way to share a web gallery with someone (via the LrMobile service) that is even easier. You just sync a collection (a right click) and then share the URL. Or another route is to subscribe to a service like ZenFolio or Photoshelter and upload JPEGs to the service. Their web gallery options are very flexible.