If your oven has a flat floor, then there are heating coils directly below. The floor gets very hot, and that would take your bacon grease (or anything else) immediately to its smoking point. Step 1 is definitely to get a roasting pan or some other such device to keep spills and splatters from hitting the oven floor.

Step 2 is to make sure the oven is properly clean. Built-up grease on the oven will definitely smoke. You could do the self-cleaning cycle, which will presumably generate an uncomfortable amount of smoke. You can also get spray-gunk at your favorite supermarket. These tend to come in two flavors: those that have lye and those that don't. Lye-based cleaners are amazing (and amazingly dangerous), and they're not appropriate for a typical enameled oven interior (as in mlord's oven photo). Make sure you get the proper cleaner. Expect to spray, scrub, spray more, scrub more, etc.

Step 3 is definitely to double-check the oven gasket. That thing needs to be intact and clean. Working properly, you can have a smoky mess inside the oven and no corresponding smoky mess outside the oven.

Step 4, get an oven thermometer and check the temperature. It's possible your oven thermostat is busted and it's generating a whole lot more heat than you need for whatever you're trying to cook.

Finally, if all that fails, get a Weber grill (or equivalent) and do the smoky stuff outside. For things that require uniform heat, get a Dutch oven which you can put inside the Weber, directly in the coals.