Is it possible to have a bowel cancer and a stroke at the same time?

Yes. The pathophysiology of one has nothing to do with the other.
Yes. Stroke can happen related and unrelated to the bowel cancer. Cancer will cause hypercoagulable state-that will increase risk for develpment of blood clots/thromboses. Bowel cancers on average more commonly occur at the middle age/older age group- the same age group where other conditions also happen - i.e. Hypertension, cholesterol , diabetes etc-which are risk factors for stroke.
Why not? Unfortunately, having one misfortunate does not confer immunity to other co-existing problems. In fact, some illness actually contribute to strokes.