Not fastest, but certainly the most efficient way.
By experience, sniping a near-dead Ragna is the fastest way to get tickets, but you waste quite a lot of BP that way. Starting your own ragna and getting enough damage to secure MVP and then inviting other people (requires some weird timing and a good solo team) will be the most optimal way to spend AP. BP-wise, look for ragna requests with at most 2 players and a full health bar.