Every member of the military must apply for a personal military security clearance.  A person entering the military does not automatically receive a security clearance; it must be formally applied for and granted.  Along with relevant personal data, the security clearance application requires specific disclosure about financial delinquencies, which include personal U.S. Division-North leaders assess combined security checkpoints in northern IraqChapter 7 and Chapter 13 bankruptcies occurring within the last seven years
It usually takes over a year from the time of security clearance application to successful granting of the security clearance.  A good portion of this time may be the investigation stage of the approval process.  During the investigation stage a credit check is performed.  If a credit problem (such as bankruptcy) is discovered, further investigation is performed which may include requests for additional information and interviews.  A PRSI, or Personal Subject Interview, is a regular part of the security clearance process which all applicants, regardless of credit history, must complete. 
Grounds for denial of security clearance include being found to have serious, repeated financial problems or intentionally giving false statements regarding your finances.  A security clearance is usually successfully granted if one can honestly present plausible reasons for financial problems in the past, including a bankruptcy.   Financial mitigation of security concerns includes the following:   behavior that happened long ago or infrequency; financial problems outside of one’s control, such as illness or loss of a job; good faith efforts to repay debts; evidence of successful counseling for past issues; and sudden affluence from a legal source of income such as an inheritance.  
On the other hand, if there are repeated bankruptcies or ongoing financial problems that are not resolved a security clearance will most likely be denied.  Often times it has been reported that underlying unacceptable actions in the eyes of the military, such as alcohol, drug or gambling problems, result in denial of the security clearance.  In addition, frivolous or irresponsible spending and an unwillingness to pay debt (as well as fraudulent or illegal financial practices) can also be cause for denial of a security clearance.  
Conclusion:  If you are truthful and specific on your military security clearance application you will most likely not be denied a security clearance if the reasons that led you to bankruptcy have been eliminated.