1) minimises splash risk
2) allows you to easily store and re-use your dye solution
All you need is a large glass jar with a screw top lid that has an internal neck diameter of around 2.75" (7cm). This will allow you to insert the larger items like wheels into the dye solution.
First clean the jar of any original contents, and then fill the jar half way with boiling water from a kettle. Then add your dye, like RIT, and in this case I'm using black. For the small quantity of water that you will be using, you only need between a 1/4 and 1/3 of a pack of the powder. Stir well to ensure that all the dye dissolves into the water.
Cover the neck with cling-film and then pierce the surface of the film to allow the solution to vent.
Then place in the microwave, if not already hot enough from dissolving the powder, and microwave on full power for about 120 seconds. The larger the jar, the longer it'll need in the microwave. I check the temperature by hand, it should be hot but not scalding (time for a bit of care and common sense here

I tie dental floss to the parts I want to dye, usually using one of the holes, and then suspend the part(s) in the solution.
After about 20 minutes, take out the part(s) and check for colour absorption. With black, I want the part(s) to achieve full saturation so I usually repeat this another two or three times. Just re-heat the solution each time using cling-film to cover the neck and pierce to allow venting, and the drop the parts back in for another 20 minutes.
Once you are happy with the colour, rinse in cold water until it runs clear and allow to dry. The Pro-Line wheel below had four 20 minute sessions in the solution to achieve maximum absorption.
Once your done, allow the jar to cool, screw the lid on and store for next time you need it. Don't forget to give the solution a good stir before you use it again and also, keep an eye on the level of the solution. The level will drop over time with use so you just need to keep it topped by adding more water up to your half way point. (Thanks to GoMachV for the reminder on stirring the solution!)
Obviously, this method does have some downsides like not being able to do a large amount of items all at once and it does take a bit longer but for me at least, it works really well.
Hope you find this useful.