The reason you only have one neutral busbar is that your panel is super, super, super small and there simply aren't enough circuits to need 2 neutral bars. Larger panels don't have 2 neutral bars for neatness, they have 2 bars to provide enough neutral/ground screws (if main panel). You shouldn't even worry about terminating the neutral on the same side of the breaker. One thing we preach a lot here is "don't save money on the panel - you'll only regret it later".
For instance, with 8 spaces, and if you totally fill it with 15A breakers, that will only be 60A (remembering the feed is 240V). Running 125A feeder to it is a complete waste of your money -- or to be more precise, this postage-stamp panel is a complete waste of your time. I would return it to the store and spend a little extra on something like a 24-space. You'll thank us later!
As far as neatness, there is no Code requirement for neatness, at least, not in the way you're about to see. What you actually need is enough slack on your hot wires so you can move breakers around without limitation, and enough on your neutrals so you can bring them to the breaker on the happy day you upgrade to AFCI or GFCI.
Grounds need only be long enough to reach the ground bar; they'll never move.
And that should be reasonably tidy; it doesn't need to be Mom's spaghetti. What the 110.12 neatness rule is saying is don't just toss it all in higgledy piggledy so it looks like a grenade went off in there. Try to comb it a little.
Here's what you don't need: this guy has painted himself into a corner.
I feel pretty / Oh, so pretty / I feel pretty, and witty, and carefree....
Whatever brain cells this guy used to style the panel, he should've used to do a better job of the actual work. For instance where's the well marked white tape on the neutral wire? That's not optional. What is optional is different color hots; better to make them both black (since they are interchangeable) and the neutral red (since it is not) and taped too. How does this "pro" not own white tape?
Look at the grounds on the neutral bar. Sloppy. This guy does main panels all daaaaaaay... and it's allowed in main panels, but sloppy and a bad habit. If neatness matters, why not use panels with ground bars, and tuck them directly out of the way first? If this panel were ever made a subpanel, a bunch of ugly wirenut extensions would be needed.
He's cut all his neutrals an inch or two too short, so he'll be either angling or wire-nutting every neutral when he goes to add AFCI/GFCI.
But those top circuits can never be moved to any other position. He's murdered all the slack. So if he needs to move things around to make them more logical, or rearrange to fit a 2-pole breaker somewhere, or he needs to use double-stuff breakers and those only fit in the bottom 8 spaces... he's cut off his nose to spite his face. Why do that? Slack is cheap.