Other than a helmet and water bottle, no special gear is necessary for day-trips, though enthusiasts may want to pack their own saddle, pedals and shoes, and if you’re cycling in and around Kathmandu you’ll definitely want a proper face mask against dust and pollution. Good (expensive) ones are sold in department stores; the cheaper ones only keep out the worst of the dust, not the dangerous particulates. Cycling clothing, shoes and gloves aren’t easily obtainable in Nepal, nor is good waterproof/windproof outerwear. Note that tight Lycra clothing is embarrassing or offensive to many Nepalis, especially when worn by women, so unless you’re sticking to the main Pokhara or Kathmandu trails, consider a pair of comfortable shorts over body-hugging bike gear.
A helmet and water bottle will come with a better rental bike. If renting a cheaper one, you could buy a helmet in a Kathmandu department store and carry your own water bottle – with something for water purification. Panniers and racks can be rented from the better bike shops, and daypacks and waist-packs are sold all over tourist areas. You can pick up bungee cords in any motorcycle accessory or repair shop.
A good lock and cable are essential, especially if bringing a fancy bike from home. Local bike shops sell cheap, less effective locks. Bring bikes inside at night. Puncture-repair places are everywhere on the roads, but travel with your own patch kit, inner tube(s), pump and basic tool kit, especially if riding off-road.