Hi @Fiona82,
Thank you for your question about drilling into a stump.
You're going to want to look at what is called an auger bit.
The longest and widest I have found that are not Special Order items are this Diablo 18 x 445mm Auger Bit and this Sutton Tools 500 x 18mm Long Auger Bit.
Please note that you are going to need a drill that can exert a lot of rotational force (torque) for these drill bits to be effective. Corded drills such as this Ryobi 800W 13mm Corded Hammer Drill will be capable and higher-end cordless drills such as this Makita 18V Brushless Heavy Duty Hammer Driver Drill with a fresh high amp hour battery will be capable.
Ensure you use the auxiliary handle (side grip) as the torque exerted can and will injure your wrist if you are not prepared.
Let me know if you have any further questions.
Jacob
