It's not possible to beat the initial rotation of the first firebar, so the best way to enter the room is to hold right and start moving down once you've cleared it.

After lifting the first pot, you can hookshot to the edge of the block, avoiding the first firebar and the moving spike. You can then take an intentional hit from the second firebar before lifting the second pot (optionally hookshotting to it to save a couple of frames) and finishing the rest of the room.

You can also elect to hookshot downward a second time to gain invincibility frames while the firebar passes through you. This is less than half a second slower than taking the intentional hit.

Without the boots, the fastest way to deal with the hardhat beetle is to carry the pot and throw it. This takes advantage of the fact that carrying an object does not slow Link down if walking on a pit edge. You'll want to make sure that you're at least one pixel away from the block to retain full speed -- being flush against the block will result in slower movement.

Using a byrnadash can save about half a second at the cost of about 20 points of magic. You can deactivate byrna (either by quickswapping, or pressing Y) immediately after clearing the firebar, to avoid any extra magic consumption.

A capedash is the fastest way through the room and costs roughly 28 points of magic. Normally you'd tap A an extra time to perform a "poof walk" to deactivate the cape while moving, but this is unnecessary in this case; if you ensure that you're at least one pixel away from the block, deactivating the cape while walking on a pit edge puts keeps you in a walking state automatically.

Without the hookshot, you can simply take a hit from each firebar while walking across the bridge, losing only about half a second.