Over at Texas Instruments, TI for short, you can find their CCS (Code Composer Studio). Get the newest version. At time of writing 7.4.something was out.
Download the on-line installer for Linux.
When the download is complete execute
$] tar zxvf ccs<version>_web_linux-x64.tar.gz
you should now have a README_FIRST.txt - do read that file.
Next execute the ccs_setup_linux64_7.4.0.00015.bin
After a little while you should see something like this:
accept the license and click Next
Choose your preferred installation path and click Next
Select the SItara processor - the one on BBB and click Next a few times more.
The installer work for qiute a long time downloading Eclipse and much other stuff. Be patient it will eventually complete.
Start the application - maybe you need an entry in your menu or you can use a path similar to this: /home/klaus/ti/ccsv7/eclipse/ccstudio
Maybe you software needs to be updated on the first launch - do that in order to have the most resent version installed.