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, wich means that its hitbox is bigger, enough to push mario backwards.
Keeping the bloated bob-omb
After grabbing the bloated bob-omb, you have to walk, then the bob-omb wil start exploding again, then you have to re-grab the bob-omb. During these small frames of walk, 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.
Teleport Hands-free 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.