As of the the time of writing, BitBucket has made a change on their side that is incompatible with Version Checker. This means that a mod's myMod.version file may not be hosted on BitBucket anymore. One of the best alternatives is GitHub, which is free and has been working nonstop with Version Checker for years.
This short guide does not require any knowledge of coding or git. We'll simply move a myMod.version file over to be hosted on GitHub instead of BitBucket.
If your online masterVersionFile is located in the "Sources" part of BitBucket (ie in git), not the "Downloads" part, then your job is even simpler.
1. Follow these steps here: https://gist.github.com/mandiwise/5954bbb2e95c011885ff#gistcomment-1833787(credit to Histidine for finding this)
Spoiler
(https://i.imgur.com/r4sSpRBg.png)
(https://i.imgur.com/HRq7Zgb.png)
2. Continue from step 6 below by clicking to open your .version file.
Otherwise, if your version file is located in the "Downloads" tab of Bitbucket, not the "Sources" tab.
1. Create a GitHub account at https://github.com/join.
2. Create a new repository by heading to https://github.com/new.
a. Set the name to your mod's name.
b. Ensure the repository is public (this is the default).
c. Click Create Repository.
Spoiler
(https://i.imgur.com/WsHCvYA.png)
3. Next, click the button to upload a file.
Spoiler
(https://i.imgur.com/yn04hoM.png)
4. And now, drag and drop to upload your myMod.version file (click "Choose your files" if that doesn't work).
Spoiler
(https://i.imgur.com/J4PeWCw.png)
5. Almost done. Add a short description of what we just did, like "Added version checker file.", and then click "Commit changes".
Spoiler
(https://i.imgur.com/SzkG85o.png)
6. Click on the file we just uploaded to open it in the GitHub viewer.
Spoiler
(https://i.imgur.com/utw8bT9.png)
7. Then click "Raw" to open the pure text file.
Spoiler
(https://i.imgur.com/qNcWZZV.png)
8. Now, just copy the url. For example, https://raw.githubusercontent.com/yourUserName/my-mod/master/myMod.version. That's the new, permanent online location for your version file.
9. You'll need to take that url and put it into your myMod.version file, replacing the old BitBucket url, and then repeat the file upload process with the newly edited file so that the myMod.version file on GitHub has "masterVersionFile" as a link to GitHub.
Spoiler
(https://i.imgur.com/kysfxZ3.png)
10. And, last step, the next release of your mod should have this new myMod.version file with the now-working Version Checker file.