The relevant definition from OED is:
Capital, first-rate, ‘crack’.
This is most certainly the definition you are looking for as, all of the citations are 1844-1875 (although the earliest of said citations are for "bully-boat"). Also, it's listed as originally American, so that fits with the "young man in Aroostook County, Maine".
A similar definition can be found in A Glossary of Words & Phrases Usually Relating to the U.S.:
Fine, capital. A low word, used in the same manner as the English use the word crack
What's cool about this source is it was published in 1860, a mere five years before the usage in your clipping.