Well you can't really change the shape of your biceps, but you probably already know that. What you can do is make them a lot bigger which will partially take care of your problem.
To maximize biceps developement I find the following to be very important:
Include some heavy work: back in the days guys that had tremendous biceps also curled monster weights. Jack Chevrier who was a Canadian bodybuilder in the 70s renowned for his huge guns (heck, even Arnold himself asked him to take a pic with him he was so impressed) and he curled 315lbs (slight cheat) and 225lbs for 12 reps! Mike Mentzer was also known for curling tons of weight. Actually, curling in the 200-225lbs range for reps was "common" by them.
Biceps respond particularily well to eccentric loading. Doing accentuated eccentrics lowered in 5 seconds is a great way to build the biceps.
Biceps are best trained with a low volume of work, but frequently. I found that myself this year.
Working in isometric work at the end of a dynamic set is also very effective. In that case you would hold the weight with the arms bent at 90 degrees after your regular set.
I feel that in your case, training the biceps 3x per week, with a very low volume of work would be best.
Monday go heavy, stay in the 4-6 reps range, you can even cheat a little as long as you lower the weight under control.
Wednesday go high-density: perform a triple set:
A1. Peacher curl 6-8 reps
A2. Reverse curl 8-10 reps
A3. Hammer curl 10-12 reps
Do this triple set 3 times
Friday go triple failure training: Select one biceps exercise with a barbell.
Perform 2 warm up sets and 1 work set:
- 6-8 normal reps to failure
- Once you reach failure hold the bar at 90 degrees for as long as you can
- When you cannot hold the weight anymore have a partner help you lift it, and lower it in 5 seconds for 2-3 reps.