Just for fun I'm really going to put the cat amongst the pigeons now: working muscle mass.
Maximum Heart Rate is just that, the hardest your heart will ever work. In order to achieve this the entire body should be working as in swimming or perhaps also running. In cycling the legs are the primary muscle groups at work and since the upper body is used to a far lesser extent one's cycling maximum heart rate is likely to be lower than one's actual maximum heart rate. Everyone with me so far?
As a test for one's cycling maximum heart rate, complete a 20 minute warm up at an easy pace arriving at the bottom of the kind of hill that makes you think twice about whether or not it's really the best route anywhere. Ride up said hill three times as hard as you possibly can. Cry at the top if you need to. Vomit at the top (you probably will if you're doing it right…) The highest figure you recorded is your MHR. It's not a fun thing to do and if you're in any way unsure about how healthy your heart is there is no way that you should be attempting to find your MHR using any method.
Anyway…to answer the original question…to increase your capacity for endurance rides…go for long bike rides. Some might suggest that going out without anything to eat would be of benefit but I'd hesitate before reccomending that because you need to have some fuel to burn to fuel you for the ride…all you'll achieve by eating nothing is making yourself hungry more quickly.
As a rule of thumb if the event is 100km aim to be able to ride 120km without flinching. That way when you get to the start line of your event you KNOW that you can cover the distance.
Regarding efforts and intervals and heart rates…such sessions are good and valuable sessions in their own right and as part of a correctly structured training programme. But from your original post I'd suggest that distance work is where it's at for now.