Bumble

Bumble is one of the youngest citizens of Little Lamplight, at 6 years old. She spends most of her time in the 'Schoolhouse' learning the history of the world as told by Joseph, or 'Uncle Joseph' as she calls him. The reasoning behind her name is that she tends to knock things over around Little Lamplight. She is wearing Blast Off Pajamas and is currently being trained by Lucy to be the town's doctor.

Her real name is Betty, which she will tell you the first time you meet her if you have the Child At Heart perk.

Depending on how you introduce yourself, she will dismiss you saying either "Mungo" or "Vault Dweller" - this changes only if you reveal that information.

When you have Bumble as a follower and approach Major MacCready, he may converse with Bumble. The conversation is along the lines of : "Hi, how are you?" "We are in the best fucking place in the entire world." "Um...ok"

Be a Child Slaver
She can be captured by the Child Slaver to get the Boogeyman's Hood from Eulogy Jones. If you bring her outside and kill the child slaver, she will go back inside and does not want to go outside again: "I don't like outside."

Bugs
After Bumble is taken by the Child Slaver outside of Little Lamplight and the player speaks to Eulogy Jones to receive the Boogeyman's Hood, it is possible to once again select the dialogue to lure a child out of Little Lamplight. Bumble will then reappear in Little Lamplight still wearing the Slave Collar and can be lured outside again to the Child Slaver. However, the dialog between the two will not unfold as it should and they will stand there indefinitely. (Verified on Xbox360)

Note: If Eulogy disappears he can sometimes be found a couple of days later picking up some profits from the town clinic at which stage he will pass back into the circulation of Paradise Falls

It is possible, though rare, that when Bumble exits Little Lamplight she will be stuck inside the rocks to the left of the entrance and the player may see her flicker. This problem can be fixed by entering the caverns again and waiting for her to follow.

If you decide to kill all of the people at Paradise Falls to free the captured Little Lamplight characters you can still have Bumble go with the slaver if you previously talked to Eulogy about capturing the kids at Little Lamplight, but if you do you don't get a reward and the characters go inside the slave pen, into the slave room and disappear.

Bumble As a Temporary Follower
It is possible to keep Bumble as a follower for the rest of the game, though it has absolutely no advantages and is troublesome. When you get Bumble to follow you outside, as soon as you exit Little Lamplight, open up your pipboy and fast travel to your desired destination, instead of bringing her to the slaver. When arriving you will see that Bumble is still with you. Technically, she can now be used as follower for as long as you like, though it would be very hard to do.

As she is only supposed to go outside once, she will not follow you into houses or anyplace that causes a loading screen. Upon returning outside, she will either have disappeared, or, in the case of walking through megatons gate, she will still be around however she wont follow you anymore, and will walk back to Little Lamplight. She can be given a weapon, however she will never equip it and always runs away at the first sign of an enemy, and will not come back to follow you once they are gone.

So, technically, with this bug you can have a permanent, essential follower with you throughout the game. This follower will never die, but will also never fight, never shoot, never follow you into buildings, can't be told to wait, can only be given equipment through Reverse-Pickpocketing and will always run away at the first sign of trouble. In other words, she is useless as a follower.