This is a tough question, one for which there is no definite right or wrong answer. In general, if someone has had a bleeding stroke (such as your father), but
has never had a heart attack or ischemic stroke (stroke caused by a clot in one of the arteries to the brain), I would say he should not be on aspirin. If he has had either of those in the past, then aspirin should be ok provided he keeps his blood pressure under extremely tight control.
Based on the description you gave, that his bleed was deep within the brain, my best guess is that this was a "hypertensive hemorrhage". In other words, likely due to a lifetime of having higher than normal blood pressure. If that is the case, far and away the most important thing to be done is to get that blood pressure under VERY tight control. As a general rule, if you add the systolic and diastolic blood pressure numbers together, the goal should be to have a total number of less than 200. If he gets lightheaded or woozy with blood pressure medicines, then this goal can be adjusted (of course, always due this with the guidance of your local physician). Blood pressure control, in his case, will be much more important than aspirin.
To summarize: If he has never had a heart attack, or other ischemic vascular event such as ischemic stroke, I would not give him aspirin. If he has had one of those, aspirin can be considered, but should be done only in conjunction with tight blood pressure control. In either case, he needs his blood pressure watched EXTREMELY CLOSELY.
I hope that helps. Good luck.