I'm 47 (and it does get harder with age) and started from zero running to passing my test which required a level of 8.2 for someone my age. That's with Police Scotland.
Have your force not provided you with a training programme? If not then I suggest this one from Police Scotland which is a 6 week programme - it will fit in with your timescale. I used it and it really is good and builds up steadily from zero. It also explains the science of getting fit and training diet.
If you're based in England then IGNORE the section about the levels you have to reach because in Scotland it's higher. In England it's 5.4 for everyone, regardless of age and gender.
I approached my training with two strategies - 1. Push your fitness to beyond the required pass level. 2. Start practicing the actual bleep test now so it comes as no surprise on the day - get familiar with it and don't fear it.
you can download the actual police bleep test audio here in mp3 format - scroll down the page. I downloaded it and put it onto my phone and played it through the music player
Besides fitness, another tactic I used was to count how much time you have for each level. At level 1 - I estimated that you have 7.5 seconds to reach from one end to the other. Level 2 - around 7 seconds, at Level 3 around 6.5 secs, etc, etc. By level 9 you have about 4.5 to 5 seconds to get from one end to the other and turn. When I was training and on the actual test day I counted the seconds inside my head at each level and for each shuttle run. This helped me keep my pace and timing so I hit the line before or on the beep. Hope this makes sense. Listen to the bleep test audio, get a stop watch and time the duration between the bleeps. It sounds a bit daft but it worked for me.
If you're in England the level is 5.4 and on the scale this is just a tad faster than jogging. By around level 7/8 you're sprinting. If you're in England consider yourself lucky, in Scotland you have to hit 9.2 to pass (for a young male). That's not being racist - I'm from England and live in Scotland. I'm envious.
Also adopt the correct mentality - you're training for the Police, not a fun run, pleasure or sport (so I keep telling my wife who runs for sport). Attack it.
You'll do it easy. All the best.