You're not going to get bulky. It's just not going to happen. I'd like you to take a look at the picture of Natalie Burgener below. She competes in the 63kg (136 lbs) weight class and has snatched over 100kg (220 lbs). She would never be mistaken for a football player.
You can bet that Natalie here trains everyday, possibly twice a day, with weights heavier than most of us would imagine using. I compete at 75kg, and have never even attempted to snatch or clean and jerk what Natalie can do on a regular basis.
What enables her, and can help you, lift incredible loads without looking like it is a matter of workout programming. Most strength athletes don't do isolation work and rarely do more than 5 reps at any given weight. At 5 reps and less, people first adapt through better muscle fiber recruitment, meaning that your body learns to coordinate itself within a muscle better so that all the fibers can work together to complete a task. Untrained people new to lifting will see marked increases in strength without seeing much change on the scale or in muscle size for this reason.
After the neurological adaptations peak, strength starts coming slower through hypertrophy, or increase in muscle tissue. If you keep your reps at this lower end you focus your adaptations on what is called myofibril hypertrophy, whereas bodybuilders and those looking to put on mass tend to work in the 8-10 rep range to get at sarcoplasmic hypertrophy.
While both types of muscle growth happen regardless, you and tilt the scale towards one or the other by manipulating your reps. Myofibril hypertrophy means that cell adaptations focus more on creating more contractile tissue to be able to handle the loads required of it. Sarcoplasmic hypertrophy means that more sarcoplasmic reticulum is created around the contractile tissue to get more nutrients and signaling chemicals to the fibers so that muscles can better handle the greater volume of work required of it. Myofibril hypertrophy tends to tilt results towards tighter, stronger muscles, whereas sarcoplasmic hypertrophy tends to create rounder, fuller muscles.
Let's say you have someone trying to get you to do exercises in the 8-12 rep range anyway. You still shouldn't worry about getting huge, because there is that pesky little hormone we all have called estrogen.
My point is, most people aren't in the gym two hours a day, six days a week. That is the kind of dedication you need to attain the look at left. For the rest of us who want to get a good workout and look great in less than an hour three times a week, you're going to have to pick up those heavy weights!