Dapper async and transaction

I'm trying to figure out how to properly use the Dapper with the transaction. But I still think I'm doing something wrong. All the examples I found are without using async.

Could somebody advise me how to do it right?

class DapperAsyncTransaction
{
    private readonly IDbConnection _dbConnection;
    private IDbTransaction _dbTransaction;

    private IDbConnection Connection => _dbTransaction.Connection;

    /// <summary>
    /// Constructor
    /// </summary>
    /// <param name="dbConnection"></param>     
    public DapperAsyncTransaction(
        IDbConnection dbConnection)
    {
        _dbConnection = dbConnection;
        _dbConnection.Open();
        _dbTransaction = _dbConnection.BeginTransaction();
    }

    public async Task Execute()
    {
        try
        {
            await Connection.ExecuteAsync(
            @"insert into Persons(Name, Surname) values" +
            "(@Name, @Surname)",
            param: new { Name = "John", Surname = "Doe" },
            transaction: _dbTransaction);


            _dbTransaction.Commit();
        }
        catch (Exception)
        {
            _dbTransaction.Rollback();
        }
        finally
        {
            _dbTransaction.Dispose();
            _dbTransaction = _dbConnection.BeginTransaction();
        }
    }
}