Yes. There is no requirement that a married couple file bankruptcy jointly when one spouse needs or wants to file and the other does not. It is very common for one spouse to file for bankruptcy while the other spouse does not.
Many couples decide to file for bankruptcy together. If both spouses have debts they cannot afford to repay, whether they owe debts jointly or each have separate debts, the law allows them to file a joint bankruptcy case. Filing a joint case costs the same amount as filing for just one spouse, and if both spouses are spending household money to pay creditors instead of buying groceries and gas, and maybe an occasional dinner out, it makes sense to file jointly.
However, if your spouse does not have debts, or has only debts which can be paid without sacrificing necessities, you are free to file an individual bankruptcy case without your spouse.