Is it permissible to pay a sum of money to obtain a Hajj permit for a woman who has been prevented from performing Hajj, and what is the solution if it is not permissible?

There is no objection to a woman performing Hajj even if she has not been explicitly granted a visa for Hajj, especially if she fulfills the conditions for Hajj being obligatory upon her. No one is permitted to prevent people from performing an obligatory act, and there is no obedience to a created being in disobedience to the Creator. If the prevention is without a legitimate religious reason, or if the woman fears that she may not get another opportunity to perform Hajj, then she must perform Hajj. The woman should explain her situation to the religious officials responsible for Hajj, and if they are unable to secure a permit for her, she should depart without bribery if possible; otherwise, she should pay the bribe, and the sin will be on the one who takes it.