You can help the development team keep up with the bug reports by closing duplicates, helping to clarify reporters’ problems, and confirming that you can reproduce bugs.
You can view the entire list of open bugs, or browse Banshee bugs by various attributes (ones with unreviewed patches, etc).
You can get e-mailed about every Banshee bug change that happens by going to your Bugzilla preferences and following banshee-maint@gnome.bugs .
It is very important to bug reporters to get a response — almost any response — to their bug reports, and quickly. It shows that people are listening, that the system works, that people care, etc. You can help provide them that response. You can manually browse the bug list, or sign up to get e-mailed for new bugs as mentioned above, or you can view the list of unconfirmed bugs that are most likely to need a response.
You may not have permissions to do much at first except comment — which you should feel free to do. You should read GNOME’s bug triaging guide.