Would be is generally used either:
to state a willingness to perform an action if certain conditions are met
or if circumstances were different.
It expresses a present state of mind about a future situation which may be realistic or simply hypothetical.
I would be travelling first class if I could afford it.
I would be willing to meet them if they were here by midday.
We would be able to sign a peace treaty if they withdrew to their borders.
It is also possible to use will be in such circumstances but it lacks the sense of reserve and politeness expressed by would be.
*Would have been** declares what might have happened in the past if circumstances had been different. That's to say, it can no longer take place.
In your example you say that on the occasion in question, you did not have time.
Therefore the possibility of meeting him on that occasion no longer exists.
Thus you would have been happy to see him had circumstances been different.
If you are talking about a possible future meeting, you would be happy to meet him.