I'd add in office/clinic nursing, possibly dialysis, school nursing, home health, case management... Most nursing jobs do involve "direct" patient care, in other words, "having contact with patients." But"bedside nursing" really refers to hospital/staff nursing, LTC, nursing home type of jobs.
As for new grads? Dialysis sometimes hires new grads, home health sometimes, too. Although I would recommend getting some "bedside" experience in your pocket. It's not always pleasant, but it does offer tons of learning experiences in procedures, disease process, time management and people skills. These will serve you well and broaden your horizons in the future.