Madeira - Port shuttle to city center?

[AtlantaCruiser72]

It's been several years since I was last in Madeira and when previously there we did a full day private island tour by jeep.  I can't remember if there is a port shuttle (free or small fee) from the large ship cruise port to a city center drop off / pick up location.  I know the walk is about 20-30 minutes, but we plan on doing a lot of other walking in town, at Monte, the Botanic gardens etc, so if a shuttle was avaible that would be helpful in maximizing time/energy for what really matters :)

 

Any helpful advice appreciated!