The fastest way to kill off bed bugs without using an exterminator would be to get some bug fog spray you set off in your home with the windows and doors closed.
Doing this will require you to stay out of your house for around 5 hours after letting the bed bug spray out of your home.
The really best way to guarantee getting rid of bed bugs though is by actually hiring an exterminator who has experience in getting rid of the bed bugs. Plus they have better methods and more powerful chemicals then homeowners can get from the store.