After talking with a few of my friends and clients who are testing for positions such as police departments, fire departments, military, and other government positions it is quite evident by some of the physical evaluation drills they have them performing are very much non-functional and very impractical to the actual physicality of the daily job duties. This is also the case with much of the country's sports training- mainly football. They look at how much a prospective applicant and/or athlete can Bench, Squat, Situps, and Run for distance. Most of these are with a one rep to three rep max. Most of these movements are not even performed in the line of duty.
Football is notorious for performing a lot of bench pressing and squatting. When in football is anyone on their back pressing someone or something overhead? Well if they are on their back it is usually when the play is stopped. Additionally squatting needs to be done very explosively in most real-life and athletic events. Practicing slow or moderately paced squats with either both sub-maximal or even maximal weight will not transfer over very well into explosive power. If you want to be explosive you must practice explosive movements. Honestly it is very unfortunate that the tests even call for bench to be performed. That tells absolutely nothing for someone's overall strength. It uses some of the body's smallest muscles to perform that lift.
Besides when in your duty as a police officer or firefighter, or any job for that matter, are you lying on your back pushing something overhead? Alright, alright I'm sure we can find a suitable bench press simulating movement in the Las Vegas area, but let's keep this one clean in the sense of what jobs require that sort of movement and stay on track. Additionally you can be in very crappy shape overall and still have a good bench number. See what I'm getting at here?
If there is no way around not testing on the bench press then I would not focus so much on actual bench as in the supportive lifting that will accompany it. Of course you must practice benching to get better at it, but not so much to overtrain. Two to three times per week is adequate for the actual performance of bench when working toward the goal of testing and then simply work harder at the supportive lifting. Then after you reach your goal and pass your test forget practicing bench. It isn't life practical and functional fitness.
For these sorts of individuals, or any who desire to become overall stronger in natural raw strength where pressing movements are concerned, I would recommend to focus on practicing several variations of pushups including handstand pushups(against a wall if you need to). If you cannot perform a HSPU then bend your elbows and hold there for a given time. Focus on overhead pressing, push pressing, and jerking dumbbells or kettlebells if you have them. This will make you very strong, fit if done properly, and bring up your bench without ever directly focusing on bench.
Handstand Pushups or Inverted Pushups work the entire shoulder structure. Don't think in terms of what muscles does this or that exercise work. Think in terms of movement and how you can get your body to move more efficiently and get stronger in each movement.
The same muscles that perform a bench press perform in pushups, handstand pushups, and any kind of pressing movement. Muscle isolation training and body part separating need to be stopped and forgotten for this will never lead to real-life fitness. Your body should be trained as a unit because that is how you use it in life. When you exercise, go to the gym, or perform any weight resistant movements that is how you should imitate it. This is exactly why I call my training Synergy Kettlebell Training. We use the kettlebell as our primary resistance tool, but in the end it is just a tool that we use and the overall movement is what truly matters. Ask any of my clients and they'll tell you that I can care less how much weight you can lift or survive a grueling session, but the focus is on the movement even if it is without anything except your empty hand. I am a firm believer that if someone cannot properly perform a given movement with just their bodyweight many times over then they have no business using weight in that movement.
The following movements will produce amazing upper body, as well as core and lower body, strength by practicing them in your workouts regularly.
Press is moving a weight overhead with the use of the arm to a lockout position without the assistance of the legs.
Push Press is moving a weight overhead with the use of the arm to a lockout position with a little bit of assistance from the legs by performing a very slight knee bend(squat) to generate momentum in order to allow the arm to work less to get the weight up. This is great when the shoulder and arm is pre-fatigued.
Jerk or Push Jerk is moving a weight overhead with the use of the arm to a lockout position with a much more leg assistance by performing a coordinated double knee bend(squat) to generate a lot of momentum in order to allow the arm to work less to get the weight up. The Jerk is great for overall strength and core connectivity in synergy within your body. Combine the Clean and Jerk for both push & pull in one movement. This is the ultimate in strength training.