Most Bizarre Hobby

I’m much too old to recall my hobbies…. maybe girls, but that was later on I guess.
It would depend. Is your character boy or girl?
My daughter used to collect dolls; she took them apart, threw the bodies away and kept only the heads; had over fifty at one time. Now she’s in medical school… lol.
My son collected crayons; he won’t use them, just kept them in a box, hundreds of them. He also loved trains; every time he saw one he wanted it. We actually caught him stealing rail cars and locomotives from stores. Later he started on toy soldiers. Now, he wants to become a lawyer.

My wife told me she collected spiders

My grandpa's hobby is to unravel thread and when I mean unravel, I mean all the way...

Some people juggle geese!

Going to re-enactments with their parents. And by that, I mean they're part of the camps/re-enacting groups. Granted, they were probably brought up with it but they get to run around at the different sites and play as well.

When I was a kid, I collected skulls, antlers, and bones. It seemed a bit odd next to my Strawberry Shortcake dolls, and G.I. Joe action figures.
I was also fascinated by spiders, bugs, and any little creature I could find in a pond or stream.

Now I keep tarantulas.

*The skulls and bones I found were in the dry stage. Very little flesh or sinew left on them.
I had a friend who collected skulls, and kept a machete in her truck for the purpose of beheading roadkill. She was in her late teens. But that would probably be a bit too gory for a pre-teen character.

Well, my grandmother used to collect salt-and-pepper shakers. I've heard of one guy who collected antique jigsaw puzzles. I myself liked to lipsync to Broadway musicals (my mum would sometimes join me). Then again, there was a character in The Wrong Box who collected eggs.

Off the top of my head

Collecting:
pigs
cows
elephants
stamps
model trains
Matchbox cars
anything/everything associated with a particular tv show

Building:
plastic models (cars, etc)
airplanes/rockets (and flying same)

wood carving/whittling
Knitting/crochet/needlework
quilling
kite flying
gardening

If your character is a girl, you might give her a hobby more typically associated with boys - or vice versa.

Try juggling, unicycling - any circus skills, really.

Alternatively, I have a friend who breeds stick insects, which I think is pretty unusual. Ant farm, perhaps? Or maybe even weirder, like worm charming.

Then there's unusual crafts - I like to bivouac, which basically means building shelters from whatever you can find. I'm getting pretty good at building small sleeping shelters from fallen deadwood and other natural materials. Most of them will keep the rain out too, provided it's not too strong and I haven't made a mistake somewhere. Most of my friends think my survival skills are pretty weird things to want to learn. I know a guy who taught me to make string from things like birch tree bark or nettle stem fibres, and he makes nets, baskets and things from the string he makes, just as practice.

Or maybe a weird musical instrument? An alpine horn, perhaps, or accordion, or maybe yodelling.

My current hobby is breeding flowers, currently tulips and bearded irises, roses are something to consider for the future. I'm also interested in breeding ornamental fish, I would have started that instead if I had the money and space. Previously I've been interested in survivalism/creative anachronism, and also all forms of visual arts including glass working, carving carousel horses, basket and cloth weaving, tapestry making and embroidery, pottery, painting, etc.

Ice spearfishing. Saw this on a local cable access channel.

Collecting butterflies and pinning them on boards in shadowboxes sounds absolutely precious, until you consider that the person collecting them is grabbing live animals and impaling them.

For a pre-teen, it can be something as simple as getting hooked on an actor on a TV show--and it could be an old TV show--and collecting photos and other memorabilia. She'd be particularly strange if she got hooked on somebody like Cary Grant while everyone is fawning over (pick the latest heartthrob).

My aunt's husband was a glassblower. He collected old board games, particularly those of the knock-hockey variety (I don't remember the real name).

He knew people who collected those glass insulators that were mounted on the arms of old telephone poles.

I liked to draw when I was a kid, mostly animals and dinosaurs and mythical creatures. I'd sometimes create made up animals. I liked to draw a lot, then after high school I pretty much quit. Tis sad, I used to be pretty good (my avi is an example of my art in HS) and had all sorts of patience for it, not anymore.

I used to collect knives. Still got a few pretty ones lying about.

That's more "disturbing" than "bizarre" to most, though.

Glass menageries

I used to collect things. Anything. I collected obvious things like trading cards or Hot Wheels, but then other things like Frisbees. I had dozens of them. OMG, there's a blue one!

Maybe the kid is a writer. Sci-fi? Fantasy? Fanfic?

Investigate customized (ooak) fashion dolls, or customized Breyer horses. Either can sell on eBay for hundreds--even thousands--of dollars if done well, and some of the top selling artists of either category are quite young.

I just recently took up armored figurine construction on the side.

Or you could do writing.

Dungeon and Dragons?

I saw something about a kid who collected the arms and legs of Barbie dolls once. If you wanna make the kid strange...