Is it possible to max every art and skill without multiplayer?

While playing through my first class, I found it pretty easy to max out most of the skills I was using. Coupled with a lot of exploration, I found myself with a decent amount of BP all the time. Now I'm going through my second class and I'm a bit more worried - there definitely is way less BP going around.

Is it possible to get every art and skill to level 5 in the game? If not, how close can you get?

I'm aware of these ways to get BP:

• get class rank ups
• find field items (mechanical, biological, archaeological)
• play online
• explore new areas (and find new, unexplored territory/sightseeing spots)

It seems like the only one that gives a repeated amount of BP is playing online (which I fully acknowledge), as the other resources are finite. Playing online is fun, but with the frequent disconnects it's more of a nuisance than anything.