Hi G,
Just went through the border yesterday and no problem at all! On 24/7!
To exit Georgia it took about 15 minutes.
Then we rode few miles to the russian side. All in all it took us then 3 h to get through, just all very slow but staff was friendly enough, helpful and professional.
To help you here are few tips.
Unlike europe where you wait your turn in your vehicle, there you don't!
First, once you are in a queue, get a form for passport control. Fill it and then walk to the hut of the passport control lady. Do not wait for the traffic to move!
Once you get your passport stamped, once again, abandon your bike. Don't worry no one will touch your stuff, no one did ours, lots of uniforms around.
There is a building on your left hand side. Go to the last office and pick up two custom forms. They are in russian only, BUT, there is a sample form in english on the wall, inside that office.
Do not put any luggage in the tick box. We did this as we have panniers but the custom lady made us refill the forms saying we had no additional lugagge.
Once you fill those forms, go to the custom office cabin at the front of your waiting line. There may be people queuing, get in the queue.
Once all is done you are good to go, as long as the vehicle on front of you can go too!
For bike insurance, you can buy it after. Once you ride out, about 500m there is a big building with shop, coffee etc.
There, you will find an office where the nice young russian lady will sort out your insurance.
There is a cashpoint somewhere as we saw lots of guys leaving the insurance office and coming back with cash.
Cheers,