Best approach to making a loaf of bread stale

Don't use a paper bag, it actually helps the bread keep somewhat longer.

Your best approach is to put it in the fridge. This is the temperature at which the starch crystalizes at the highest speed.

Update, shamelessly stealing from Tristan: If you cut it up first, you will speed up the process too. The more surface you have exposed to airflow, the better.

You'll still need to give it time, but it's maybe half the time it needs at room temperature.

It may not behave exactly the same as actual stale bread, but a reasonable approximation can be made pretty quickly by slicing the bread (to expose the crumb and allow moisture to escape), placing on a wire rack so the bottom also gets airflow and baking at about 140ºC (290ºF) until it starts to dry out and firm up (check it after 10 minutes)

Even with the rack you'll probably want to flip the bread occasionally to keep the sides even. Thankfully this temperature is low enough that the bread shouldn't start to brown or burn so you shouldn't need to worry about accidentally making toast instead (it should also end up with a much more even level of drying, unlike toast where the inside is usually meant to remain soft and moist)

Thinner slices will dry faster, but may be less suitable to later stages of your recipe. If you're going to be turning the bread into breadcrumbs or similar though, you probably want to slice as thinly as practical