Use this principle;
Give your bullet the following behaviors;
a) Drag & Drop
c) Bullet (initial speed of 0)
1) Pin the bullet to the character using rope-style.
Combined with the Drag&Drop behavior, you will be able to move the bullet around like in angry birds by dragging.
2) On Drag&Drop (when the player drops the bullet);
a) Unpin the bullet
b) Disable Drag&Drop
c) Set bullet speed to a value (can be based on distance to character)
d) Set bullet angle of motion (based on angle to character)
The sling part of the system is just a visual trick. It doesn't actually serve any mechanical function.