Bill Masen is a kind of everyman character, certainly not the kind of lantern-jawed superhero we might expect to find in such a scenario. Calm, rational, and utterly logical, he's able to see through all the chaos and work out what needs to be done at every turn.
While so many others are running around in a state of panic, Bill's able to keep a cool head, largely because of his training as a botanist. Bill's scientific background allows him to see the triffids, not simply as giant carnivorous monsters, but as objects of study. For it is only through studying them and their behavior that mankind can be saved from a full-blown apocalypse.
Just as it was science that helped create the triffids in the first place—bio-engineered in a Soviet laboratory—so it will be science that must figure out a way to destroy them. That's why it's important that the rational, analytical values of people like Bill Masen must prevail, even though it was the abuse of such values that brought about this almighty catastrophe in the first place.
What is interesting about novels like The Day of the Triffids and their ilk is that the focus is on the creation of a dystopian world which has replaced the order and normalcy of our world today with chaos and disorder. One of the problems with many dystopias is that this emphasis is only achieved at the expense of developing convincing characters. Often characters are left rather vague and undefined. You might like to consider The Handmaid's Tale by Margaret Atwood as an example of this.
However, having given this caveat, it is clear that the character of Bill Masen certainly develops throughout the course of this excellent novel, as he is involved in various groups of post-disaster humans, which allows him to comment critically on the various groups and responses of humans to the disaster that has befallen humanity. For example, the groups of Michael Beadley and Wilfred Coker have a very different response to their situation and their responsibility towards blind humans. However, gradually we see Bill Masen developing into a character who is not happy to be merely led but wants to lead, and this is seen in his desire to search for Playton and his decision to run the farm with her in Sussex. He has gradually transformed into a leader.