Biceps make up the smallest muscle on your arm so you don't necessarily need to train them constantly, it'll just be overtraining and can have adverse effects. When you do other pull motions such as back, rear deltoids, etc. you are working out your biceps at a secondary level. You can work them out a 2nd time if you feel you want them bigger later on in the week but you definitely don't need to be working them out for 1 hour.
For getting results, once you've hit a plateau its more than just adding weight, workout movements are learned movements and once your body is used to them, it doesn't have the same effect. Its time to switch it up, but it can be also a matter of changing things other than weight, change your rest time, change your tempo, change the number of sets you do and the amount of reps. People can't just keep going up in weight, you need to consider other factors as well.
For the first exercise of your workout I'd suggest either standing barbell curls or preacher curls, do 3-4 sets of 6-8 reps. Your second exercise can either be hammer curl, alternate dumbbell curls, zottman curls, preacher bench dumbbell curl, etc for 3-4 sets and 8-10 reps. Your 3rd exercise should be either concentration curls, machine curls or cable curls for 3-4 sets of 10-12 reps.
If you want your arms overall to look bigger not just your biceps, concentrate on your triceps as well, they consist of 3 different groups and the biggest part of your arm, once they get big enough and stick out they make your arm look much bigger, don't forget the forearms either, the bigger they are, the bigger your arms look.
Hopefully this helped you a bit, if you didn't understand anything let me know I'll do my best to translate in French, I just know this stuff much better in English.
