Hi Dal,
Yhe M40 engine is easy enough to bleed. I have never seen a Haynes manual, so cant comment on that but this is how I would do it.
Move the heat setting inside to hot with the heater fan off. Open the stat bleeder and remove the filler cap. Remove the rad bleeder. Fill with water until it comes out the rad bleeder, then replace the bleeder but only tighten 2 turns. Run the engine at idle and fill with water again. I would use water as its cheaper than coolant and there is no point in wasteing coolant at this stage. As the engine heats you will see air/water from the bleeders. close them and leave the engine running. keep an eye on the temp, as long as it does not boil it is ok to get as hot as it likes. As it heats, watch the temp of the bottom hose. When the stat opens this will heat up in a few secs. At this stage open both bleeder again to allow the air which was behind the stat to escape. The one on the stat only needs to be opened for a few secs, the one on the rad for a few seconds longer. Be careful not to overtighten the rad bleeder they only need a pinch to seal. You can open either bleeder a couple of times for a few seconds each if you like to be sure. At this stage put the cap back on on drive it for about a mile. Then let it settle to allow the pressure to drop and carefully open the cap. Top up if needed and run for a few mins more, opening the bleeders a couple of times for a few secs each.
You will now be ready to check it for overheating. If it is ok, all you have to do now is drain the system, refill with coolant and bleed it all over again :)
Bear in mind that a blocked rad will make bleeding more difficult.
HTH
Alan.