The only required use of the Bait Bag in casual play is in Bird's Peak Rock, where you are supposed to use a Hyoi Pear in order to trigger the switches to unlock the door leading to a triforce chart. It is possible to trigger all switches using bow snipes except the highest one and as such, it isn't possible to skip the bait bag in a glitchless speedrun.
In 100% speedruns, the Bait Bag is a required item to get. However, there are tricks to skip a few hyoi pears. The various Hyoi Pear skips will also be documented on this page.
Normally, the Bait Bag is required to enter into Bird's Peak Rock. However by grappling the grapple target from a relatively lenient position, you can clip through the wall that blocks your way into the grotto hole by pressing A to cancel the grapple as you swing backwards into the wall.
It is possible to hit the switch at the top of Needle Rock without a Hyoi Pear. To do so, stand next to the cave (that is under an ice block) and aim with your bow to the sky. There is always a kargarok standing next to the switch. Hit that Kargarok with a fire arrow and he will be sent back into the switch. A Kargarok in fire being able to trigger switches, you will be able to get the chest.
Note that this only works by hitting a kargarok with a fire arrow. It will not work with any other arrow type, and it will also not work if there is no kargarok on that ledge. Also note that this trick is also possible on the other side of the island, since there are two kargaroks on that ledge, one on either side.