I recommend you leave both of those as neutral bars, and add some accessory ground bars, which are $6-ish, each. Otherwise you will run out of neutral bar locations long before you run out of spaces. Neutral bars are hard to add.
At the very least, use the left one for neutrals. It has a better chance of being able to support all the breakers this panel can support. You can never double-tap neutral lugs. But many panels will allow you to triple-tap ground bars, which means you would be able to get enough grounds out of the right side bar.
Also, since this is an outbuilding, it needs a disconnect switch. Where is it? If you have none, and this panel is convertible to main breaker, that would suffice. Otherwise you'll need to either backfeed a breaker, fit a separate disconnect switch (generally more expensive) or use a different panel.