Won't fit in a CRJ bin, might fit in one of the closets (if installed), but traditionally the CA has first dibs on the cockpit closet (I think that's too small anyway), and the FA's use the cabin closets (for their stuff and premium pax coats). If it were one leg nobody would mind, but as ongoing thing it would be an imposition.

So really you'd have to gate check it every leg. That's a PITA with multiple legs but can be done. The problem is if they miss the gate check tag, it will go to baggage claim and then are you going to delay the flight to go outside security and fine your bike, or abandon it. If you make a habit of it, it WILL get sent to baggage claim eventually, probably sooner rather than later.

I wouldn't worry about what people think in this case, crew sometimes bring guitars, golf clubs, skis, snowboards. But other than guitars it's usually only *sometimes*.