Bullet engines are dry sump engines (as were most early British motorcycle engine designs)
This means there should be very little oil in the bottom of the crankcase when the engine is running.

The bulk of the oil is kept in a separate chamber at the rear of the main engine casing (where you top up the oil)

The RE has two oil pumps (although they are on the same shaft) which work on a disc valve arrangement.
They are situated on the timing side just above the oil filter housing.

The first oil pump draws oil from the tank and pumps it through the hollow crankshaft and so to the big end bearing.
(big end of the connecting rod and probably the most highly stressed part of the engine)

The oil is then flung off the big end and "splash lubricates" the crankshaft bearings, little end bearing, cylinder wall etc.
It then falls into the bottom of the crankcase and is sucked out by the second oil pump.
As the second pump has a larger capacity then the first one, the sump is kept "dry"
The second pump delivers the oil to the rockers (via that external pipework) and it dribbles down the pushrod tube and into the timing chest.
From there it goes back to the oil "tank"

Wet sumping is when the crankcase fills up with more oil than it should while the engine is at rest.

This can happen if oil finds it way by gravity from the oil "tank", through the oil pump and out of the big end bearing.
It can also find it's way from the timing chest through the timing side crankshaft oil seal or direct from the oil tank via a bad crankcase gasket seal.

If the sump is "wet" when you start the engine there is far to much oil flung around inside the crankcase as the crankshaft will be dipping into the oil.
It can come out of the engine breather with messy results.
Oil also gets up into the combustion space as there is too much oil around for the piston rings to wipe away. This causes the engine to smoke.

After the engine has run for a few minutes the (larger) scavenge pump will clear the excess oil and all returns to normal.
By then you can have oil all over the back of the bike from the breather, and a smoke screen to annoy the neighbours.

What to do about wet sumping

1. Leave the engine at TDC when it's idle.
   This puts the big end bearing higher than the level of oil in the "tank" so oil can't get through by gravity.
2. Don't overfill the oil "tank" - about half way on the dipstick is fine.
   

If you still have a problem it may be the oil pump discs need lapping in or the crankshaft oil seal is leaking.