Sidebar Login Test:
Theme: WordPress 2011
WordPress Version: 3.4.1
BPS: BPS in BulletProof Mode
Test Time/Duration: 8 minutes
Result: Not conflict or problems exist between BPS and the Sidbar Login plugin.
Dragged the Sidebar Login widget to my sidebar in Appearance >>> Widgets. Logged out of the testing site. Logged in successfully using the Sidebar Login Widget. I did not test with using the alternative template tag use: To use the template tag: Add <?php sidebarlogin(); ?> to your template.
The login process does not automatically redirect me into the wp-admin Dashboard area on login by default, but 3 links: Dashboard, Profile and Logout are displayed in the sidebar and of course the new WP top Admin Bar is displayed. Configured login redirect by going to Settings >>> Sidebar Login and added a redirect login link. On login i was successfully redirected into the wp-admin Dashboard.
Since everything worked fine in testing then most likely you have a combination of things that is causing a conflict. Please post a link to your website so i can see what might be the specific problem occurring on your website or you can send me the link to your website - info[at]ait-pro[dot]com if you want to keep your website anonymous/private.