That route is pretty much what I'd do. I rarely cycle in Central London because it's horrible, and I don't know anything about superhighways, but as it happens I rode pretty much this bit of route last weekend when I test rode the route.
Here's what I'd do (with landmarks)
Head West out of Bethnal Green til you come to Shoreditch High Street/top of Bishopsgate and turn left.
Keep going South past
Liverpool St Station on your right.
Then bear right on Threadneedle St, and head towards
Bank.
At the confusing junction at Bank keep going straight on Queen Victoria St. You will probably get it wrong and have to get off and cross a ped crossing.
Then at Mansion House bear right a bit onto Cannon St. Ride past
St Pauls on your right.
Now it's mainly a straight line to where you're going.
Cross Farringdon St and the road you're on changes to Fleet St.
Keep going straight (no need to wiggle round the Aldwych) past
King's College/Somerset House on the left and come to the N end of Waterloo bridge.
Now the road you're on changes to the Strand.
Keep going straight and go past
Charing Cross on your left.
At the roundabout (
Trafalgar Sq on your right) take 2nd exit (Whitehall) which leads down to Westminster bridge
Basically, from Bethnal Green, go left onto Bishopsgate, bear Right on Threadneedle St then try to keep going West.
So mine is very slightly different. But not very. Expect to get a bit lost around Bank.
