To begin with you have to understand that, contrary to common belief, arms do not belong to a family; they belong to a person and his/her heirs with appropriate differences.
Secondly, to do this assignment you will have to document the paternal bloodline backwards through each generation and cross check the first-born son in each generation. This is a time (and cost) intensive research project for which you would have to bear the cost. Any competent professional genealogist should be able to assist you in this endeavour.
Burke's General Armory (and the 'General Armory Two' ) lists 15 entries in the surname of Bull. However, most of those 15 are unlikely to be related unless the record notes 'same arms'.
If you contact me via email at gjksau [@] yahoo.com.au I can let you have a copy of those 15 records to assist your search.