Bob-ombs are enemies in SM64. When they see Mario, their fuse lights and they start chasing him. After their fuse ends, they explode, creating an explosion object.
The bloated Bob-omb is the state when the Bob-omb gets bigger, right before exploding. Usually, this Bob-omb explodes. But if you grab it right before the explosion, it will be delayed for 12 frames. Note that if the explosion is early (by throwing the Bob-omb on the ground) It won't explode until the timer expires. The explosion is delayed, but the Bob-omb stays big, which means that its hitbox is bigger, enough to push Mario backwards.
Maintaining a Bloated State
After grabbing the bloated Bob-omb, you have to walk, then the Bob-omb will start exploding again, then you have to re-grab the Bob-omb. During these small frames of walking, you will be able to turn.
Another way of keeping it is by holding it Hands-free. You will be able to jump, double jump and ground pound. You can't turn except if you have a Wing Cap, where you will be able to fly while being pushed backwards.
Hands-free Teleported Bloated Bob-omb
If you teleport while holding a Bob-omb Hands-free, This Bob-omb will disappear. But if you go close to the first teleporter or if you teleport back, the Bob-omb will appear in front of you, giving you backwards momentum while keeping almost every movement. You can grab that Bob-omb by diving or punching. Kicking will cancel the momentum.