No, I'm not trying to make a smoker, I'm trying to keep my oven from smoking

If the slightest drop of any type of food gets on the bottom of our oven, it starts smoking and sets off the smoke detectors. Recently, I tried baking some bacon instead of putting in in a pan. The results were phenomenal, but the process resulted in having to hold our doors open for about half an hour, and the entire house filled with smoke and smelled like bacon for a day or two (which isn't as pleasant as it would sound - especially when you're trying to fall asleep).

Is there anything I can do to mitigate it? I'm currently cooking the bacon on a cookie cooling rack over a drop pan. Would lining the drop pan with bread to sop up the dropping grease help? Is there anything I can do?

Unfortunately we have no vent. Well, the microwave above the stove does have a vent mode, but all it does is take air from beneath it and shoot it out the front. It doesn't go outside or anything.