I've only been training for around 9 months. I've been stuck on the same weight for bench press for over a month now. I'm following Scott Herman's 12 week program at the moment, before that I used to do 3-4 sets of 8. 

Many people have said that switching to dumbbell bench press for a while could help, would that be a good idea? If not, what could I do? I can steadily increase my weight on all other exercises but not the bench press. I've been paying extra attention on the form so I'm pretty positive that my form is good.

That great your are building overall strength I suggest you to work more on your shoulders and triceps. becz these are the parts which are also engaged in barbell bench press. increasing strength on triceps and shoulders with gradually help you lift more not only on your bench presses but in other exercises aswell. switching to dumbell presses is also a great idea to bring more stability and good range of motion in chest exercise. But once my gym instructor said that barbell bench press is the king of all exercises so dont quit on it. keep working your best and soon you will be able to lift your desired weights on bench.

May be your grip is too wide or too close, it is said that in a bench press your elbows need to almost 90 degree with your arms and your chest. and bring down the bar on your middle part of chest. if your bringing it on neck or too low above your abs its a bad form. But you feel that your form is correct Its better to ask a gym buddy to film you when you are doing bench press this way you can compare your form of bench press with scott's proper way of doing the bench press correctly if there are any flaws you can counter them. I have tried this method and it really works.

Some good advice above. I will say keeping your arms on bench press at 90 degrees is super stessfull on your shoulder, you can still do them and they have their place but 45 degrees would be better. Although it takes a little from your chest you will use your triceps more and move more weight, also push through your heels on the way up. Chest Presses to the kneck have their place too but are dangerous and hard on your shoulders as well.

 

Mainly if you've been doing the same thing for 9 months switch it up in case you have plataeued. More reps, different exercise ect. If you cant increase weight then something needs to change. Try a deload week. You may need a good break for your muscles and CNS.