In my opinion, bridles or any tack for that matter (even the human intervention per se), cannot cause collection. On the contrary, it has great potential to prevent it.
I'd like to give an example from the human world. On my daily way to work, I have to take the metro. It can sometimes be quite a shaky ride and people often stumble, when they don't hold on to something.
Now, if you try to stand without holding on, you'll see that it's actually quite easy to do - if you take on a somewhat collected stance. You'll just need bended knees, more tension in your body and a little room to balance.
So why is no-one standing 'collected' in the metro (except children sometimes)? It is, in my opinion, a combination of factors:
First, there's an environmental factor: it is seemingly easier to hold on instead of engaging the whole body and if there is something to hold on to, I take it. There is no motivation to do otherwise.
Second, there's a physical factor: office work, or just walking on the street is not enough to activate my muscles in a way that I feel good about physical work.
And last but not least, there is a psychological factor: it might look rather strange if I tried to balance in the metro. It is far more common and normal, if I press myself in a corner and hold on tight.
This example might sound far fetched, but for me it is exactly what we deal with in horse training.
Horses are often not in the best physical shape so that collection would come easy.
The environment (or tack) is often not helpful as well, as it restricts free movement and doesn't puts the horse in a mood for natural collection.
And finally but most importantly, the horse needs a motivation to move collected. In nature that can be fighting a rival, showing off, or playing. Everything else (fear, insecurity, feeling pressurised, boredom, ...) blocks the free collection and works against it.
In my experience with Mucki and Lily, I found that they actively WANT to collect. IF the conditions are right.
Then even the heavy load of a rider is not necessarily hindering the collection, but on the contrary a challenge and collection comes logical to them, because they need the tension to carry that load.
So to come to an end, I'd like to say that it's not really the collection that needs to be trained or worked on, it's all about the preconditions. Then, collection comes naturally