This weapon can make it easier to defeat a Rainbow Bird, because of its special effect.
Bemusing Arrow is the one weapon that both Shana and Miranda must both use if the player is giving them their best weapon available. The next is the Virulent Arrow from Kashua Glacier and the previous is the Long Bow from way back in Kazas
Is a rare drop from Arrow Shooter in the Barrens. Because so many areas lie in between the Barrens and Fueno, there is additional incentive to wait for the considerable amount of time it will probably take to get it to drop. Shana will not be able to buy it until Fueno, four hours or more away, but it would might take an hour or more to get it to drop. The encounter rate for the Arrow Shooter may or may not be the same on the two screens, and that there is arguably better farming in the Home of Gigantos, an hour and a half away. Fighting the Rainbow Bird, which is the Bemusing Arrow's ultimate utility, cannot be done until after Fueno. Shana can definitely use this increased grinding time to get to her maximum SP gain, and there is not much time left to use her before she is removed from the team.
If you do decide to kill repeatedly for it ("farm" it), know that it matters quite a lot whether you go to the second screen in the Barrens, or stay on the first one (spoiler info on the Barrens page)