One long engine/frame bolt to go, but its not moving which led to this question.
In general, should the pressure be applied to the bolt head and the nut held in place,(my thought), or the other way around?  And of course, it probably really doesn't actually get sperated that way.  
While it would seem that twisting off the nut is normally the thing that we do, that is because it's what we usually can get to.  when dealing with these long bolts, both ends are available but -  the threaded portion should be structurally weeker?  
Pragmatically, I ask as I have to buy a socket for 1/2" drive and as the bolt head and nut are different mm's, just gathering your thoughts..
Of course, if i had some money I'd simply by a set of sockets
Heavy rains this am in central Mass - but thankfully not up to MidWesten standard.  My wife and i send our sympathy to any of you hit by that disaster.

Suggest getting an impact wrench.  If you don't have an air compressor, get the electric version.   Helps prevent shearing the bolt...   I got a small Air powered 3/8" drive one from HomeDepot that had lifetime garrantee.  Used it to rebuild my engine.   I think it was around $40.

As to the question of which to turn.  Turn the side that does not have the lock washer.  But,  once free it doesn't matter.   Also, Coarser thread bolts shear sooner.    And....WD40, Liquid Wrench or CRC is your friend!!!!!!

After 40 years of doing something this basic, I've forgotten where I've heard it or if I just reasoned it out.

Turn the nut, hold the bolt.  But in some cases it turns out to be turn what turns, hold what don't.  

ratchet on both ends works for me

Pawnshops have tools. A used impact is as good as a new one in 5 years. Barring some kind of abuse, but a lame impact will handle everything Ive had to do so far. There are sockets, individually available, often by the pound instead of piece. Harbor Freight has a set of 1/2" drive impact metric sockets pretty cheap. 6 pointers. I got some, no more slop than high class ones. I have tools from many makers & in some places, the need for higher quality justifies the expense. Some places, cheap works fine. I think the Harbor Freight impact sockets are plenty well made for the kind of use they will see maintaining this little bike. A small compressor just means taking longer, its still a lot easier than without air & going back together with the clutch, having air meant I didnt have to back up the motor to tighten the clutch pack, just a quick blip on the trigger.

BTW, Ingersoll Rand impacts have an incremental; trigger & can be run slowly, which can be helpful, especially if a wobble socket is on it. Most, like Chicago Pneumatic are wide open or off. This is where I spend the $$$. Ingersoll Rand 1/2 & a Mac Tools 3/8ths, and an air ratchet3/8ths, I think its a Mac, also, but one of the sweetest tools in the box is the 1/4" air ratchet. Made swappi9ng the radiator out on the Honda Civic a non knucklescraping deal.