The only required use of the Bait Bag in an any% speedrun 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 bug limit speedrun.
In 100% speedruns, the Bait Bag is a required item to get. However, it is possible to get every heart pieces without ever buying a Hyoi Pear. The various Hyoi Pear skips will also be documented on this page.
Go to Bird's Peak Rock (quadrant G5). Position yourself to the far left of the grated passage way, on the pictured texture, and pull out the grappling hook. Aim it into the cliff until you see the targeting icon appear. Grapple to the post, and as you begin swinging back towards the cliff, immediately let go to clip through the gate.
Get chest storage and bomb boost up the ledge on BPR. With chest storage you can sidewalk past the gate and enter the loading zone early.
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.
The HP at the top of Headstone can be obtained without flying as a seagull thanks to chest storage. First, get chest storage anywhere on the ocean and superswim (or sail) to Headstone Island. Get to the western ledge with the leaf. You can climb the island by manuevering a specific way and get the heart piece.