First, make sure you meet all of the prerequisites set by your squad. Prerequisites may include length of service, specific training, and above average annual reviews.
Second, get your foot in the door early. Talk to current squad members and let them know you're interested in this type of work. Try to attend a couple of bomb squad training days to gain a good understanding of what the job entails. When it comes time to test you may have your foot in the door because the team already knows your name and that you've shown some interest.
Also, my team was looking for some investigative experience, and specifically an officer with crime scene investigation experience. I'm currently assigned to detectives and have been a CSI for years. In that time I took a couple of arson and post-blast investigation classes to help prepare myself. The bomb squad is responsible for post-blast investigation so any training along this line should help.
My testing for the team included a written test, an oral board, and a practical exercise. The practical exercise consisted of operating in the full bomb suit and completing a series of tasks including carrying X-ray and disruption equipment a couple of hundred feet, then getting down to ground level and setting up the gear, and finally walking back to the start.
If it's possible, I recommend that you get dressed in a full bomb suit before the testing so you will have some idea if you can function in the suit.