A slow progression like you are doing is the absolute best way to progress over the long term. It is possible to progress faster, but that often mean that you will have to sacrifice long term progress.
As for the suggestions posted earlier, 5/3/1 uses a very slow progression model, which is great for long term progression as I just mentioned, but it will no give you super fast gains.
If you are at 85kg for sets of 8 reps it means that your maximum for 1 repetition is about 110kg and thus your current 5RM (maximum for 5 reps) is around 93-95kg.
My 915 program should take your 1RM to somewhere between 120 and 125kg, at that point your theoretical 5RM would be 102 - 106kg... maybe you could hit 110x5 under the proper circumstances.
It would likely take you about 12 weeks to reach 110kg x 5 (915 is 9 weeks long and add 3 more weeks of double progression using sets of 3-5 after the completing of the program).
You could likely reach your goal faster if you decided to focus only on the bench press and putting everything on maintenance level. This would mean using something like the Smolov junior program but do it for the bench, it might allow you to get there in 6 weeks.
This program has you bench pressing 4 days a week. To make it work for the bench press you'd have to decrease volume for the rest of the body and especially for the shoulders.
It might look like this:
First test your max bench. I actually want you to do 3 bench press tests in a week. Test on monday, wednesday and friday and make an average of the three.
For example let's say that on...
Monday you reached 107.5kg x 1
Wednesday you reached 112.5kg x 1
Friday you reached 105kg x 1
Then your "max" would be: 108kg. That's the max you will use to calculate the training weights.
Why test 3 times? Because your maximum fluctuates and if you test it on a very good day you might overestimate it and make the program impossible to complete. Also because the program calls for 4 weekly bench sessions so you want to use a max that is done under similar circumstances.
Bench press 6 x 6 (see loads below)
Week 1: 70%
Week 2: 70% + 2.5kg
Week 3: 70% + 5kg
Week 4: 70% + 7.5kg
Week 5: 70% + 10kg
Other muscles trained: legs
Bench press 7 sets of 5 reps
Week 1: 75%
Week 2: 75% + 2.5kg
Week 3: 75% + 5kg
Week 4: 75% + 7.5kg
Week 5: 75% + 10kg
Other muscles trained: back & biceps
Bench press 8 sets of 4 reps
Week 1: 80%
Week 2: 80% + 2.5kg
Week 3: 80% + 5kg
Week 4: 80% + 7.5kg
Week 5: 80% + 10kg
Other muscles trained: none
Bench press 10 sets of 3 reps
Week 1: 85%
Week 2: 85% + 2.5kg
Week 3: 85% + 5kg
Week 4: 85% + 7.5kg
Week 5: 85% + 10kg
Other muscles trained: chest and triceps
Note that the work for "other muscles" should be minimal, just enough to prevent losses. When you do a specialization program you cannot train the rest of the body hard.
On week 6 you'd try to peak for the 110kg x 5 test...
Bench press 110kg 5 x 1 with short rest periods (30-45 sec)
Bench press 110kg 2 x 3 (60-90 seconds of rest)
Bench press 110kg 3 x 2 (60-90 sec of rest)
Test 110kg x 5
Understand that this is a specialized approach. DO NOT use this plan if your priority is to build overall strength.
It should allow you to reach your objective rapidly BUT it is not ideal for long term progression or developing overall body strength and size.
If you decide to do this program do not forget to increase your calories significantly.