BOSS just shells out the report in HTML or text format. It still functions. You can configure BOSS in the GUI not to issue a log on completion, or select the option to show it in your text viewer of choice. One can always choose another program as an HTML vewer anyway.
I run my BOSS in IE11, no problems but unfortunately must needs to run Wrye Bash as administrator as there is something http://www.gamesas.com/topic/1525110-wrye-bash-thread-104/#entry24127112 with WB and UAC here.
Try running WB as admin (losing the Installers drag & drop) and check the advanced settings of IE (http://answers.microsoft.com/en-us/ie/forum/ie11-iewindows8_1/frequent-message-internet-explorer-restricted-this/ae82d989-c143-404b-bba4-22e91c880b32?auth=1 but I have it off because it offers a prompt) as well as the security settings. Running IE in protected mode (and 64 bit protection) might also help.
Edit: Meh the text view not working so well. Facelift required.