I think (and this post backs it up) that you should not need to specify the public key with connector/net
to require SSL. This should work:
"Server=SERVER;Database=test;Uid=UID;Pwd=PASSWORD;SSL Mode=Required;"
Specifying the public key is only needed to ensure that the server you are making the SSL connection to is the one with the corresponding private key. Otherwise, with none specified, it will carry out a standard SSL handshake with whatever certificate the server in your connection string presents.
So you still get an encrypted connection, but you do not additionally verify that the server you are connecting to is one you previously installed the public key for.
If you still need to do this, you can try loading the pem file with BouncyCastle.