|>>|| No. 2891
The joy of electronics is that it doesn't give a damn if you're trying to build something trivial, the same rules still apply.
I think you should reduce R1 (possibly to zero), or you'll be pissing away volts across, and power into, the transistor. You want the transistor on hard. As it turns on, the voltage available through the switch will drop, as more volts appear across L1. No need for a current limiting resistor on the base, by the time the transistor is on enough to pull the bottom of the inductor to 0.6V or so, it'll all self-limit.
Bear in mind also that 9V batteries are shit. Alkalines start out at 10Ohms, end up at 1K. Make sure your doorbell solenoid won't just drain it in a couple of uses. A battery holder with 6 C cells has vastly better performance if you can find the space. (or 4 C cells, given that the pp3 will be wilting pretty much from the start).