The limits on behavior known as harchakot are designed to minimize the chances that a couple will slip while the wife is in niddah. During niddah, even our non-physical expressions of togetherness need to be weighed against any physical response they might elicit.

In Shulhan Aruch Yoreh Deah 195:1, we learn that a husband should not "play" or be "light headed," meaning frivolous or flirtatious, with his wife while she is in niddah. What exactly constitutes playing or light-headed frivolity is subject to different interpretations. Some rabbis permit playing games together. Others are stringent. Still others permit such games only when there is a 'need' for it.

Your conduct here depends on whether or not bowling leads either of you to excessive frivolity, to explicit thinking about intimacy, or to touch. If it does not, then you may go bowling during niddah.