Hi Judith,
Adding the raster to the map, displaying zero values as transparent, and then publishing it to Enterprise from the table of contents in Pro works (right click on image layer > Sharing > Share as web layer). You would choose the Tile option under "Copy all data," as suggested above by @Katie_Clark (see screenshot below). In the configuration tab of the Share as Web Layer pane, I've been having good results selecting the ArcGIS Online/Bing Maps/Google Maps tiling scheme and then adjusting the level of detail to meet my needs.
Note that the publishing may be fairly quick, but building the tile cache can take a long time. Don't judge your final result until that tile cache building process is complete. Good luck!
- Holly