I am no power lifter, just an average weekend warrior golfer who wants to gain ten pounds of muscle. I am 6'0" and weigh 166 pounds. Does anyone out there believe I can do it simply by doing bicep curls, tricep curls, military presses, and exercising my legs on the bike machine (at different levels of difficulty)? I am hoping I can try to add the weight through using heavier weights at 6-12 reps. per set; 4 sets per workout, 2 days a week.

Definately not with that routine. Read the stickies mate

What NBS said. And the bike certainly won't help you gain weight. Also, have you added surplus calories to your diet?