Currently, the bitbucket-branch-source-plugin does provide support for branch sources from BitBucket Server repos, but only for BitBucket "project" repos, not BitBucket "user" repos.

In other words, it supports repos that look like this:

$BITBUCKET_BASE_URL/projects/$PROJECT_ID/repos/$REPO_ID

but not repos that look like this:

$BITBUCKET_BASE_URL/users/$USER_ID/repos/$REPO_ID

Currently it looks like the plugin simply takes the "Bitbucket Server URL" field from the config, appends "/projects", then appends the "Owner" field from the config, then appends "/repos", then appends the "Repository Name" field from the config.

The simplest means of solving this may be to extend the base URL out to include /projects or /users, but that would probably be a breaking change (unless you sniffed for the substring after the last /).  Otherwise, I guess you could define, in config, if it was a "Project" repo or a "User" repo in config.