We used National Express bus service a few years ago and found it an easy 2-hour ride. However, you should allow a minimum of 5 hours between the time your flight arrives at Heathrow and your flight out of Stansted. At Heathrow, you'll have customs, immigration, pick up luggage and get to the bus stop. Then a 2-hour ride. Then you'll need 1-2 hours pre-flight at Stansted. Check rates, schedules at www.nationalexpress.co.uk. Also there is helpful information at www.londontoolkit.com. If money is no issue, a taxi or private driver would be simpler and faster.

And don't cut it close because easyJet is very strict about their check in times.

You've got no control over whether your flight will arrive on time, how long it'll take you to get through immigration and what the traffic's going to be like on the M25 (Europe's busiest road, which accounts for most of the journey between Heathrow and Stansted). The M25 between Heathrow and Stansted is a very great deal less predictable, and buses very, very, much slower and less frequent than between Heathrow and Gatwick.

However much slack you build into your planning, there's still a risk you'll miss the connection, and a prebooked car will still be exposed to the same traffic problems as a bus. It can't go any faster than the bus, there are no clever back road options and it'll hit the same jams: the ONLY advantage is not having to wait for the next bus.

If you miss your connection, you'll have lost the money you've paid already and have to buy an Easyjet flight the following day (their Munich flights are very infrequent) at the extortionate prices they charge the day before flight. Or just possibly, find a Germanwings connection vis Cologne, or a flight to Stuttgart followed by a train, at an equally extortionate price going the same day.

Like the man said: do you feel lucky?

Personally I'd transfer at Heathrow to whichever of BA or Lufthansa offered through-ticketing from my home airport, or not mess with London at all.

There really is no sensible reason for exposing yourself to the gritty uncertainty (and potential need to negotiate a new mortgage) of a multi-airport cross-London connection to get to Munich.

Totally agree with taking BA or another airline from LHR, even if it costs more than U2. In the end the hassle and stress of getting to STN will negate any cost benefit IMO. Are you sure it's half the cost of BA, did you add cost of checked luggage/speedy boarding etc? Often these things look cheaper at first glance but by the time you add the extras the saving might be very small.

In addition to BA and Germanwings, take a look at Air Berlin, they have some direct non stop flights from LHR to MUC as well (depending on time of day/date which was not mentioned in the question.)

Where are you coming from?

Unless you are using BA points, there are lots of ways to get to Munich without going through Heathrow at all.