Sounds like everything is on track for your beans
Bean blossoms come in many colors, white, cream, yellow, pink, purple, orange or red depending on the variety.
You don't need to pollinate them - they handle it on their own. One day the flower will drop and you will see a teeny, tiny baby bean there instead.
How long it takes will depend on conditions and variety. I usually grow soup beans so I don't pick until the vine dies, someone else should be along to give you an idea on how long before you can pick them.
Happy eating