Is it permissible for me to go for Umrah without a mahram, knowing that I am committed to the booking and the money cannot be refunded?

If this is the obligatory 'Umrah of Islam, there is no impediment to your travel to perform it, provided that the companionship is trustworthy and you do not fear any harm to yourself. This is a view permitted by the Shafi'is, Ibn Taymiyyah, and the Malikis. However, if the 'Umrah is not obligatory, then your travel is not permissible. And if you have paid money and are unable to reclaim it, and your travel is not permissible, then seek your reward from Allah, for His pleasure lies in refraining from travel.