Ulis will log most of the minutes at the point (20-25ish). My assumption is that he is not going to all of a sudden become a lights out shooter, and that will limit his role slightly.
But he brings 1. Experience 2. Toughness 3. Solid Passing Ability 4. Rebounding 5. Limited Turnovers 6. Strong Defense 7. Excellent FT shooting and 8. Pretty Good Ball Handling
If he can convert a reasonable percentage of his bunnies (layups, floaters, short jumpers - like 5/6 feet), it will help immensely. If he can be "not bad" from everywhere else, I think we are in very good shape.
If Bowen just steps in and lights the court on fire, then it would be a welcome sight. But just not likely. He can gain confidence and minutes over time and bring a different element on the offense side. I project 10-15 minutes per game.