I've answered this question (in other forms) a few times - even here on Sharecare. :-)
My first question is what do you mean by "bulky?" Will lifting weights increase your muscle mass? Depending on how you train and eat, yes. Men can "bulk up" more than women - thanks to hormones. Women who just lift heavy and train hard, and do NOT add steroidal support, won't look "man-ish." But they will have some enviable arms come summer. So, the simple answer is "no."
Different training protocols will send different messages to your body (and your muscles). A qualified trainer can help you design a program that's right for you and your goals. But don't be afraid of looking "muscle-bound." Be proud!