How important is it to fully close a static shielding bag that contains static-sensitive components? Is it good enough to fold and tape the bag (with what kind of tape?), should a double-fold be used, or are the zipper-style bags better?
A shielding bag gives best protection when closed and fully surrounding the components or board within. It has two functions - 1) to shield against electrostatic field, and 2) to protect against direct ESD to the ESD susceptible parts inside. A typical bag is a laminated material having some insulating layers to stop ESD curent flow through the material, and a metallisation layer to provide electrostatic field shielding. Inner and outer surfaces should be static dissipative (or in some cases may be conductive) to prevent charge build-up.
If you fold the bag do not crease it as this may break the metallisation layer and impair the protection. A loose single fold, held by a label or tape is fine. However, remember you don't want to be using ordinary high charging tapes within an ESD Protected Area. Avoid having component leads puncture the bag.
Never staple a bag as this gives a route for ESD to pass through and make contact with components inside.
A zipper style bag is fine.
A very useful article on ESD bags is given here