By taking Epona out of bounds, you can bypass the rocks on the way to Lanayru Twilight. This allows you to skip bombs and Goron Mines.
The trick works by interrupting Epona's fall with a cutscene. Epona will continue falling past the void plane during the cutscene, so that once the cutscene is over, you can ride Epona around on the bottom of the map. The trigger to enter Lanayru Twilight is an air trigger, so riding Epona underneath the trigger will cause the the cutscene for entering Lanayru Twilight to play.
Ride Epona into the corner past the Bridge of Eldin. Walk off the ledge and immediately use a bottle item (milk, potions, lantern oil, etc.). If using lantern oil, make sure the lantern is at half capacity or below. Once on the map floor, ride around the wall and towards the bright area in the green texture.
Ride Epona into the corner past the Bridge of Eldin. Try to approach from an angle that puts Epona as parallel to the ledge as possible. Hold target and zoom the camera out a bit, then turn slightly left, back up a couple steps, and slowly walk forward until Epona's walking speed increases. Turn Epona to the right until Link's head is lined up vertically with certain markings on the top of the mountains (see Gymnast86's video), back up until Epona starts to drop slightly, and then call Midna. Make sure not to skip the text until the word "mountain" fully appears at the end of the second line in Midna's first text box (the text will vary on other languages). If you skip Midna's text too early, you will void out. Once on the map floor, ride around the wall and towards the bright area in the green texture.
If the birds are after you, you can still do the trick as normal without killing them. The birds cannot hit you at all if you hold ZR to have Link duck. Alternatively, you can stop on the bridge and let them catch up before continuing to get them to stop following you.