From my (recent) experience with my brother's late model HD, you'll likely wait longer for the job to be completed at a local shop, and the hourly rate will be similar to that of a dealership.
Have you looked at YouTube videos? The repair you describe should be relatively simple to fix as there is little in the way of diagnostics, e.g., the problem is pretty straightforward--and common to vehicles with small engines.
I would check online to ascertain whether the part or parts needed for the repair are available, and set aside some time (your time costs you nothing) to make the repair. Additionally, you may want to check out the following sites: lilhonda.com, and planetminis.com. Both deal extensively with ATVs and minibikes; there are MANY experienced hobbyists willing to help with technical issues.
Hope this helps . . .