Spoiler warning right here. If you haven't seen the most recent episode of Doctor Who, turn away right now.
Okay, I'm really starting to think I'm right about Clara being an extension of Bad Wolf. And I have more evidence. If you haven't read the first part of my theory, go ahead and click through to read Clara Oswin Oswald: A Theory in Progress.
And here's a link to the third part of my theory: Clara Oswin Oswald: Part 3
First off, the repeats of red and roses in her scenes. Scrolling through my Doctor Who board on Pinterest I came across this little gem of a Tumblr post. (Really do click through then come back here because I don't have enough text to keep it straight with all the photos.)
So looking there, you've got a red dress in Asylum of the Daleks. Roses in the background of her ship in the same episode. A rose in her hair in The Snowmen. The word Rose on the pub sign. And a red dress again in The Snowmen. Also in The Snowmen is a rose possibly carved into Clara's grave marker.
See? You can only see one glove in this shot, but it's there.
And the one that takes the cake, that really makes me think I'm right?
It's given back to him just before Clara uses the song lyrics "hungry like a wolf" to (possibly) calm down the Ice Warrior and end the standoff.
Directly after which the Doctor remarks, "Well now we're safe."
Now they're safe. Because of Clara. Just like Rose as Bad Wolf wanted to ensure. And if the doll taken out of the Doctor's pockets was really a reminder of Rose in some way, that he got it back just before Clara accomplished the task she was designed for, then there's a connection there.
I also want to point out (and I have no picture nor direct quote on this) that in "A Good Man Goes to War" River points out to the Doctor that there are worlds who revere him. Her point is that in some of these Doctor=Great Warrior. But couldn't we also argue that these worlds hold the Doctor up as a god of some sort? If so, then looking at the meanings of Clara's three names (from my last theory post), she really could be a smart friend and helper to a god. Taken in that context, Bad Wolf was protecting this god from the false gods who would supplant him.
She's keeping him safe by always making sure he has a friend around to keep him from the Time Lord victorious state. (We could seriously argue that it was Bad Wolf who led Donna and Wilf to the Doctor all those times.)
And now for the crown of this theory. We've already seen that Rose/Bad Wolf is capable of far greater influence and foreknowledge than this.
How would Rose know anything about Donna and anything about how the Doctor viewed her? He didn't meet Donna until "Runaway Bride," immediately after losing Rose to the alternate universe. The only way she would know is if she retained a little bit of her Bad Wolf knowledge. Just enough to once again keep the Doctor safe by bringing Donna into his life. And keeping her there when time got rewritten.
But the events of "Runaway Bride" led directly into "Smith and Jones" where Martha ended up keeping the Doctor safe at various points. And then we can argue that Bad Wolf led Wilf to the Doctor in "End of Time" when it came time for the Doctor's greatest threat. Wilf helped the Doctor and helped Bad Wolf keep the Doctor safe. He tried to make the Doctor let him die. But the Doctor couldn't. Couldn't let that happen. So he did what only a Time Lord can.
In essence, Bad Wolf has been (arguably) responsible for the Doctor's safety since she was created. So it makes sense, then, to think that perhaps Clara has something to do with Bad Wolf.