Strapping lass
The anatomy of the bra book goes into a detailed look at each component of the bra, here is a little excerpt from the strap section...
...The strap can come in one continuous length, or can be divided into two sections, the front section being called the front strap, and the back section being called the back strap. Bras with larger cups often have the strap split into two with the front strap having no stretch to help reduce the bounce of the breasts. With the strap being split in two this also provides the designer chance to embellish the front strap...
When thinking about your front strap don't just limited yourself to self covered straps. Here are some views of what other designers have done in the past.