Hello!
I have visited St. Petersburg in 2009 with my girlfriend on an overland motorcycle trip from Italy.
We got into Russia at Estonia / Russia border (right past Narva): it took about 2.5 hours in total but only because there was an Estonian bus in front of us and all the passengers were checked one by one.
The Russian customs officers were very professional, no hassle at all.

Different is our experience when returning back to the EU (Finland): there was a woman (customs officer) who really bothered me because my passport was not in perfect conditions (it had some small folds at pages' corners...) but at the end we managed the situation with no major hassle (no bribes were asked).
Her male collegues were much more friendly, and one of them (with higher degree) waved us out of Russia even if this ball-breaking woman told us to wait for another document's inspection (you can imagine my satisfaction in that moment ...).

I also confirm what Tony P told you as concerns the traffic police: out of 140 km (about) from Narva to St. Petersburg, we ran across 8 police checkpoints, but none of them pulled us over because we were respecting the speed limit.
The only time I had to ask road informations to a cop, he was friendly and helpful.

In case, if you change your itinerary and enter at EST/RUS border and ride the road to St. Petersburg, pay attention to a small checkpoint some km. past the border: there is only a small aluminum cabin on the gravel right side of the road with a STOP sign on it.
STOP ABSOLUTELY: there's some patrols hidden behind that are always ready to chase you.
Stop there, feet on the ground, ask permissions to restart to the cop inside and he'll wave you beyond.
Pay much attention, because it's not so visible and immediate to spot (you can confuse it with a cabin for road workers...).
As written above, we found it while riding with direction Narva-St.Petersburg, but easily there was another trap like this also in the opposite direction.

Weather: in august 2009 it was hot as hell, so no particular winter outfit.

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Nick and his 2010 Yamaha XT1200Z Super Ténéré