Holly bushes grow to be quite large. A bush less than two feet from a house can threaten the foundation, given enough time. Furthermore, holly bushes grow back even after all their branches are cut off. Some of the options for getting rid of the holly bush are to remove it and its roots with a backhoe, pull it out by rope with your car or poison it. This last option by far takes the longest.
The One-Day Effort
Rent a backhoe to rip the bush up by the roots, or cut it down to a stump to be pulled out by car. Use a chainsaw to cut it down to a stump.
Dig down into the roots in order to have a gap under the stump to thread a rope through. Wrap the rope around and under the stump.
Tie the rope to a solid portion of your car (not merely the bumper) and try to pull the stump out.
If the first attempt fails, cut through some of the roots of the holly bush with a hatchet to reduce the resistance, and try pulling again.
The Long-Term Effort
Prune or saw the shrub as close to the ground as possible. Hammer a copper spike vertically into the center of the trunk. Copper spikes are available at hardware stores are are used to hammer down copper roofing. Do this in autumn or winter, when the shrub's nutrients (and therefore the copper) are pulled into the root system. This will help kill the root system.
Cover the stump of the holly bush with an opaque tarp to deprive it of sunlight.
Another option is to pour bleach into the stump and around the roots for several days, or to pour salt into the open stump. However, this will harm the soil around the holly bush.