Okay. In all honesty, the original thought of Ms. Frizzle being a Time Lord/Lady was not my own. (I'm sure I'm not the first for the Mary Poppins one either, but. still.) It actually came from a couple of randoms. The reasons they said so were simple:
Boom.
Ms. Frizzle happens to look
just like River Song. Coincidence? I think not.
Here are some more reasons for Ms. Frizzle being a Time Lord/Lady:
1. She's always traveling inside the Magic School Bus [TARDIS], which, while looks like any other ordinary school bus, is a whole lot more.
2. She always has Liz. [COMPANION {Even if not in the same way as the doctor. =p}]
3. "Wacky Clothes" [FEZES AND BOWTIES]
4. Laughs in the face of danger.
5. Wahooo! [CATCHPHRASE]
6. Magic School Bus is a sentient, shape shifting, shrinking, time travelling machine that's went to both the Jurassic Era and to space. Thrice. [TARDIS]
7. Unusual gadgets. [SONIC SCREW DRIVER]
I'm sure there are plenty of other reasons as to Frizzle being a
Time Lord/Lady, but we're going to be moving onto Mary Poppins now.
1. She's British. Hello.
2. Unusual outfit, including bowties, scarves, and her special hat. [FEZES AND BOWTIES]
3. Strange Creatures, such as dancing penguins or singing birds. [DALEKS/CREATURES/ALIENS]
4. She may not
seem to have something to represent a TARDIS, but did you ever notice that she never flies In any other outfit than a particular dress? Aaand what color is that dress? Blue. TARDIS blue. Seems to me people underestimate the blue threads.
5. Her umbrella is a multitude of things. Not just as to do its assumed function. [SONIC SCREWDRIVER]
6. Has a purse that's bigger than it seems. [IT'S BIGGER ON THE INSIDE]
7. Supercalifragilisticexpialidocious [CATCHPHRASE]
Aaand I'm sure there are plenty more for her as well.
Both have their own style, complete with catchphrase. Both enjoy strange creatures, adventures, and taking "humans" on those adventures. Same as the doctors.
Mary Poppins and Ms. Frizzle are Time Lords/Ladies. And there's nothing you can do to change my mind.