A pickup without a bobbin is usually called an air coil. To wind them, you need a collapsing fixture to hold the coil in place till they are coated with an insulating material such as tape or wax. There have been several pickup models wound with air coils. One example that comes to mind is the Dan Electro pickups that had the coil wound directly around the bar magnet and insulated by cloth electrical tape. Other models I’ve seen are the Burns model pickup used on the Burns guitar manufactured in England. I’ve wound older single coil Epiphone pickups with magnet wire again wound directly around the bar magnet. Usually coils without bobbins have nicely fabricated covers in which they are fitted.