First transfer your route files from your GPS device to your computer. Check the manual of your GPS device for instructions on how to transfer your file.
Then continue on Bikemap: When clicking on the button "New Route" choose "Upload GPX/KML file". Click further on "Upload file" or drop the file into the drag and drop zone.
Bikemap works with GPX and KML files. Select the respective file from your computer and wait until the upload process is complete. The uploaded route will open in the route editor, where you can make adjustments by moving the track points and adding a title, description, bike type, points of interest (POIs) and images to your route.