You shouldn't need to use a separate app. It should work by default with the built-in iphone mail & calendar.
Verify which part of it isn't working. for example
- are you able to create an appointment in your calendar on outlook and then see it show up on the phone.
- are you able to create an appointment on your calendar on the phone and see it show up on your computer
The most common problem would be the first one works but the 2nd one doesn't. If that is the case the the culprit is usually that the iphone has the "default calendar" set to some other email account, or saving them just on the phone. If you go to settings, then calendars, then choose the default as your BU address it should fix that issue; As follows:
1.
2.
3.
If that still doesn't resolve it, and some things show up when others don't then the fix is usually to remove the account from the iphone settings and then re-add it back in.