Will she bear a sin if she goes to Hajj while her husband has a large debt and he refuses to accompany her?

The ability to perform Hajj is a condition for it. If you have the financial ability to perform Hajj, and the debt is on your husband, then this does not prevent you from performing Hajj. However, if you are the one responsible for the debt, then if it is due immediately and takes precedence over Hajj, it must be paid first. If it is a legitimately deferred debt and you are confident in your ability to pay it when it becomes due, then the debt does not prevent the obligation of Hajj.

If you have not performed the obligatory Hajj and your husband prevents you from traveling, you must perform Hajj if you are able and find a mahram or a trustworthy group of companions. In this case, you will not be sinful. However, if you intend to perform a supererogatory Hajj, you are not permitted to leave without your husband's permission.