Stopping and talking to the Deku guards in front of the deku palace is tedious, as well as a time waster. However there are a number of different methods, that can be applied in a variety of situations, to get past them quicker:
Hover Method (MrGrunz): One of the easiest ways to get past the guards is to simply do a single bomb hover followed by a backflip to get over them.
Superslide Method (MrGrunz): Doing a superslide to get past the guards is a bit faster than hovering. For full optimization, get ISG then preform the superslide.
Recoil Flip Method (MrGrunz): A recoil flip is an extremely easy way to surpass the guards. Using a chu or the blast mask makes this faster than hovering, and only a little slower than a superslide.
Fence Hop Method: Compared to the first three methods, this doesn't require any explosives. From the floating bridge, jump onto the fence on either the right or left of the guards. From here, simply backflip over.
Zora Clip Method (Kaztalek): The fastest way past the guards. Make sure to be out of the guards text range, and as a zora, hold Z and press b. Immediately press A to jumpslash, and you will move forward, clipping past the guards.
After going past the guards, it is possible to immediately go to the monkey's chamber without planting the magic bean and flying between platforms above the palace gardens. There are 2 main methods of doing this:
Get ISG, then go into the room on your left facing the Deku King's chamber. Go forward and do 1 chu hover onto the fence, then do 2 more backflips to land on the higher portion of the fence and then the flower platform. Put on the Deku Mask, then burrow into the flower and fly to the right over the high wall. Once you clear the wall, start flying toward the deku flower platform directly in front of you and use that flower to fly up to the monkey. This method must be done extremely quickly to get to the flower platforms on time, and can be very tricky due to the awkward camera angle.
This method is a bit slower and more explosive-consuming than the first method, but is less precise and generally easier to learn. Hover up onto the first flower platform as in the first method, then put on the Zora Mask and do a roll jump to grab the high wall on your right. From there, carefully walk over, get ISG, and do 2 hovers up to land on the platform that will take you to the monkey's chamber.