Instantiate IDataAdapter from instance of IDbConnection

I have an instance of IDbConnection, which can be any connection, Sql, OleDb, etc. I want to make a generic wrapper so I can just send the wrapper a connection and get a nice set of methods for easy manipulation. I have a Query method, I want it to return a DataTable, so I can do

IDataAdapter adapter = new OleDbDataAdapter();
adapter.SelectCommand = myCommand;
DataSet ds = new DataSet();
adapter.Fill(ds);

The problem is I have to use OleDbAdapter and it wouldn't work for SQL, I don't really want to write "driver specific" code. Is there a way I can get a IDataAdapter instance from my instantiated IDbConnection object? I know I can create a command doing

IDbCommand command = _connection.CreateCommand();

It's only logical to think there must be some easy way to do the same with an IDataAdapter.

EDIT:

using (var reader = command.ExecuteReader())
{
    var dataTable = new DataTable();
    dataTable.Load(reader);
}

Well not exactly what I asked for but a nice solution.