Get the water out of the bowl first
If there's no water, then there's no splashing! There are two ways to accomplish this.
1. Using the supply valve
Assuming that the water supply valve is accessible and the toilet is a siphon type (with a tank on the back), try this:
- Turn off the water supply
- Push and hold the flush lever, and watch the bowl -- as soon as you see the siphon kick in (the water starts to drain quickly) release the lever. The siphon will pull most of the water out, and if you time it right, no additional water from the tank will flow in to replace it (even if you don't time it just right, the level will be lower than it was before). The rim jets* will also not run, reducing water level in the bowl.
- Do your business into the (mostly) empty toilet bowl
- Turn the supply back on -- you'll hear the tank filling in the back
- Once the water stops running, flush (if you flush too soon there might not be enough water to empty the bowl)
*How the rim jets work:
When the supply line enters the tank it splits in two directions -- there's one outlet for refilling the tank (the fill valve), and then the refill tube directed into the overflow pipe to supply water to the rim jets which rinse the bowl (source):
By turning off the water line, you're preventing water from going to the rim jets, which reduces how much water goes into the tank when you flush.
Finding and operating the supply valve
The water supply valve is usually on the wall, but sometimes comes up out of the floor, and may be behind the toilet and hard to reach.
Toilet water supply will either have a knob that you rotate until it stops -- either a quarter turn, or a couple of rotations:
Or (less often) a plunger that you pull out:
You'll probably want to use a paper towel since the knob will be gross.
2. With a bucket of water
This is impractical, as you're unlikely to have a bucket with you, and even if you did, you might draw unwanted attention filling a bucket and carrying it with you into the stall in a public restroom -- but it is effective! It will also work on any type of toilet.
- Fill a bucket with about a three to four liters of water
- Pour it into the bowl quickly
- The siphon will activate, and the bowl will drain
Here's a video showing a plumber using this method to empty a toilet before performing repairs.