One Inch. The bars are one inch in diameter.
Now, you need to make sure you're getting grips that are made to slip over the throttle sleeve.
Some grips are made for Harley (and other bikes?) and may have the throttle sleeve built into it. I have not been able to discern if an HD throttle sleeve will fit the LS650. It may work but I'm not going to be the first guy to jump in that pool.
The LS650 throttle sleeve has a series of ribs molded long it's length. You'll need to remove the ribs. I did mine by taking a coarse file and placing the throttle sleeve in a vise and filing. It took about 5 minutes. Other people have done that while it's on the bike, but it makes a mess and little bits of plastic will get everywhere.
Good Luck and post pics.