Travelling is no bar. In fact many people with ostomies travel extensively, from business/work related trips to camping trips to cruises to plane excursions around the world. Take along enough supplies to last the entire trip plus some extra, double what you think you may need. Checked luggage sometimes gets lost, carry an extra pouching system and other supplies on the plane with you. When traveling by car, keep your supplies in the coolest part, and avoid the boot. Seat belts, once adjusted comfortably will not harm the stoma.
When going overseas, apart from the obvious extra supplies, you may like to take referral lists for physicians and medical centres, and some medication to control any diarrhoea and stop the fluid and electrolyte loss. When going through customs or luggage inspection, a note from your doctor stating that you need to carry ostomy supplies and medications by hand may be helpful.