Can you put gears on a dirt jumper bike?

Answer 1

You can, but with some difficulty. You'll need a new rear wheel and a shifter to start with. Then it's the dropout width. To fit external gears you need 135 mm spacing. Internally geared hubs can fit in a narrower spacing. Then for external gears you'll need an adapter claw, or a derailer with built in hanger. These effectively make the dropout thicker, so you need to use a solid, nutted axle and not a quick-release one.

Your frame is probably missing the cable stops otherwise used for the shifter cable, but for external gears this isn't much of an issue. You can run full-length casing all the way from the shifter to the derailer and just zip tie it in place.

If you go with an internally geared wheel these usually require a cable stop on either the seat stay or chain stay. After market cable stops are available, but they're specialty items. Expect to order by mail and have to wait for it.

All together, unless there's something really special about the bike it's probably both cheaper and simpler to sell the bike you have and buy a geared bike instead.

Answer 2

Dirt bikes gets thrown around a lot, so gears are likely to get damaged.

On top of that, they're ridden on basically flat(but lumpy) ground, so you don't need gears to tackle big hills or anything.