I believe read/write permission should go well with the account that you're using to back those db's of your's onto a shared path. If you know how to configure the security part then fair enough, otherwise ask your administrator to look into it. Pls. use "sa" account to run all your jobs unless there is a specific need to drift away from best practice.
I would also agree what other experts have mentioned over here, instead of backing it up on the share...try backing up on local disk, and then by using robocopy you can actually dump that file to the specific shared path. This way your backup will not be interrupted, and you'll be safe :-P