Has your dog been tested and found to truly have a lack of tear production? If he has then he should be started on cyclosporine, which is not a steroid but an immune suppressant medication. This medication is needed for life. Tacrolimus was another medication, but has been limited in availability. In addition to the cyclosporine you can use Celluvisc, an artificial tear that you can purchase at the drug store. This can be applied IN ADDITION to the cyclosporin 2-4 times daily (or really as often as needed).
Please have your dog seen by a specialist though because you want to make sure the only issue is actually “dry eye” and not entropion, distichiasis, etc. which are also common in bull terriers and can occur concurrently with dry eye.
Please do not just take internet advice if you have not seen a veterinarian yet as eye conditions are not only painful but more difficult to control if poorly treated for too long. Bull Terriers are not a breed for the owner without deep pockets:(