The changes also see musician Daniel P Carter's rock show moved from an early hours slot to a three-hour early evening place on Sundays.
The station says the move is to provide an "alternative to the various Sunday night TV talent competitions".
Radio 1 controller Ben Cooper said the changes, which also affect sister station 1Xtra, were in response to budget changes which were "hurting".
The overhaul, which will kick in on September 1, is to make savings which are needed as a result of the last licence fee settlement.
Bowman, from Anstruther, Fife, joined the station more than a decade ago.
Others who will leave include Nihal, Mike Davies, Jen Long and Ally McCrae.