Must I admit having started (but not finished) an MS when applying for a competitive PhD position?
You will need to disclose your enrollment in this unfinished master's and provide whatever transcripts or other documentation might go with that.  It's up to the scholarship committee to decide whether this disqualifies you.  If it's later discovered and they decide it was disqualifying and should have been disclosed, you're not going to want to try defending that since the whole point of not telling them is so they wouldn't know.

It's possible they may consider you to be still within their definition of holding a bachelor's only.  Lots of people start things, then don't finish for lots of reasons.  If you only have a bachelor's, there's a good argument that that's all you have and that you should meet their definition.  The committee may also be a lot more interested in what you did instead of finishing the master's.

Good luck.  But you will need to disclose.