From Sunday 1st September, all journeys on FastCat Service 350, Hull to Scunthorpe will run from Hull Paragon Interchange direct via Park Street onto Anlaby Road. Some times will change.
https://www.eastyorkshirebuses.co.uk/september-service-changes
This will mean that city centre stops, including those at Princes Quay, on Carr Lane and at Midland St will no longer be served. I would advise passengers from those stops to either walk to Paragon or catch an alternative bus to either Paragon or Hull Royal Infirmary in order to change for a service 350.
If using only Stagecoach services, a Day Out ticket is available for £9.30, which will be valid for a transfer in Hull City Centre. This is only £0.30 dearer than a day return from Barton to Hull. If using EYMS buses, then cheap fares are available from Hull City Centre to Hull Royal Infirmary. These are somewhere in the order of £0.40.
Buses towards Scunthorpe generally leave Barton around 6 minutes earlier during the times they currently serve Hull City Centre. This is due to the journey from Hull being accelerated through running via Park Street. Also note that the 16:40 from Hull is now retimed to depart at 16:45.