There isn’t a way to read Jumpbridges for like making a jb map via esi, but if you go in game on the map, the jump bridges that you have access to are colored with a green line between their two respective systems. If you take some time and write down each jumpbridges connecting system pair, once you have them all written down you can take that list to Dotlan, you can go under the navigation section and map out the bridge network in dotlan, where you can then share it with others via a hyperlink. When the other person clicks on the share link, they can “subscribe” to the network and it will be accessible for them too. You would take the network once completed and you could use it to map out your route using The dotlan route tool.
Important note: you will need to create a dotlan account to do this, as will everyone who uses this method by the shared link. Luckily it’s free and easy, can even sso!
P.s. I know this is explanation may not make a lot of sense, so if you would like, you can evemail me or I can ping/add you on discord, and give you a visual guide. My discord is Bill Ramen REDUX#6759