How to defeat the Bell Beast in Hollow Knight: Silksong
Find and free Silksong's Bell Beast to unlock fast travel

Unlocking Silksong's version of fast travel has to wait until you pick up the Silkspear Crest in Mosshome. And then you have to defeat the Bell Beast before you can ride it.
Where to find the Bell Beast
You'll find the Bell Beast in the upper left corner of The Marrow. It's trapped in a room just above where you'll buy The Marrow's map from Shakra.

The easiest way to get there is to start in Bone Bottom. Head right until you enter The Marrow and then start climbing. At the top of the first large room, hop up one screen and take a left. You'll come to Shakra. Rest on the bench next to her, and then head left and up one more screen.
Take a right and follow the three arrow (chevrons) sign to find the Bell Beast.
How to defeat the Bell Beast
Use your new Silkspear to clear the cobwebs trapping the Bell Beast. The freed creature will immediately go into attack mode (ungrateful) and burrow into the ground.
All you're trying to do in the first part of this fight is dodge the Bell Beast when it dashes across the screen and duck under it when it jumps. The difference between the two attacks (?) is the sound it makes before it pops up from the ground.

If there's no sound, it's going to pop up, pause for a second, and then dash straight across the ground. Take a few steps away from it, and then jump. You'll have enough room to move back the way it came and avoid damage.

If there's a throaty growl before it pops up, it's going to jump. It'll pop straight out of the ground and into an arc that will take it all the way across the screen. Stay on the ground and stick to the middle of the arena. Follow the Bell Beast as it lands. It'll skid to a stop with its butt up in the air for a second — enough time for you to land a hit or three.

Keep repeating this process long enough, and it'll get mad and add a new attack. For this one, it'll pop out of the middle of the arena and launch two huge, bouncing bells. After their initial bounce, they stick close to the ground, so you can hop right over them.

After a bit more dodging and ducking and bell-hopping (not bellhopping), the Bell Beast will get even madder. From now on, large bells with become a constant problem. The Beast can stay underground and roar, causing a bunch of bells to drop from the ceiling, or a single bell will drop after each jump.
The good thing about these bells, though, is that they only bounce once, and then drop off the screen, so you can just run away from them while you're preparing for the next attack.
It might take you a few tries to get all of the timing down, but just stick with it. Once the Bell Beast is subdued, you can start unlocking the fast travel points as you explore.