No. 4 barrels don't get bedded. The receivers don't very often either.
Is this a full military configuration rifle or a bubba'd rifle? Either way, check the headspace before you do anything else. Thousands of Lee-Enfields have been assembled out of parts bins with zero QC. Not even checking the headspace to ensure the rifle is safe to shoot. If the headspace is bad, you need to fix that first.
To work on accuracy, start by slugging the bore. Hammer a cast .30 calibre bullet through it and measure the bullet with a micrometer. This will tell you the diameter of the barrel. No. 4 barrels can measure from .311" to .315" and be considered ok. Larger than .315" and the barrel is shot out.
If the barrel measures ok, use a bullet that is as close to the measurement as possible. Factory ammo usually has a .311" bullet or a .312" bullet. .313" and .314" bullets can be had from .303british.com/. Add the W's.
You should be posting this kind of question on the Milsurp forum too.