I was interested to see for myself what Barack has been up to in the Senate since 2006. Turns out the Library of Congress is a good source for this info.
Here are the bills Barack has introduced. Not "co-sponsored" but is the primary sponsor or author, meaning these are directly his ideas, rather than support of someone else's proposed legislation.
None of these actually became law. Reviewing the types of bills he has authored is somewhat entertaining.
Now you can go to this page:
You can also query by co-sponsor (he didn't write it, but he supported it). Turns out 8 bills he was a cosponsor of eventually became law. Many of those laws had tens of cosponsors.
As for bi-partisanship he co-sponsored a bill by Sen Enzi (R-WY) rewarding a congressional gold medal. He helped Orin Hatch (R-UT) pass into law a traumatic brain injury program.
One bill that became law, he was the soul cosponsor. He and Durbin (D-IL) wrote a law to recognize a PO in Fairbury, Illinois, as the "Dr. Francis Townsend Post Office Building". President signed it.