Go to your mapmyride's activities page and click on the ride you want to upload to Strava. You'll see a TCX button. Click that, your data will be downloaded; then you can upload it to Strava. Make sure you remove "txt" at the end of the file if you're using a Mac. Click on the orange plus sign in Strava to initiate the upload process. Upload activity > file > choose file.

This works with individual rides. I don't know about exporting data in bulk if that's what you're asking about.

HTH!