It doesn't seem very helpful that I'm the only one with permission to read the report. Do I need to now track down someone else to look through it?
Apport decided that the attachments/logs/etc you submitted automatically in that bug report may contain information that compromises your privacy.
In time (usually within a few hours, certainly with a few days) then an automatic process will look through your bug report attachments, "retrace" them (which I believe both helps the developers find useful information, but also can remove personal information) and finally marks the bug as public.
To expand on fluteflute's answer, which is mostly right, the automated retracer does not set the bug public. It merely adds a stack trace to the bug so that it is more clear where the problem lies.
The sensitive information is kept in the bug report, as it can be invaluable to a developer working on a fix. The bug is reviwed by members of the ubuntu-bugcontrol team who will evaluate the bug and either keep the bug private, and assign specific developers, or remove the sensitive information if it is not helpful to solving the issue, and then mark it as public.