I will be traveling to Zurich by bus (Flixbus) and I'm going to need the locker facility at Zurich main station to keep my luggage. Am I required to buy a train ticket to use the locker facility?
No, the lockers are available to everybody.
The lockers are coin operated.
If the luggage does not fit a locker you can leave it at the left luggage office.
If you leave the luggage in a locker for too long it will be moved to the left luggage office anyway.
There is more information in this discussion.
Left luggage does not generally need a train ticket. You might have arrived by train and surrendered the ticket, but want to store luggage while you sight see, for example.