Should I get married before filing for bankruptcy or after?

One spouse can file for bankruptcy without the other spouse having to do so; however, this is probably something that you should consider doing first.  For one thing, for purposes of qualifying for the means test, in a situation where only one spouse files, the income and expenses of the non-filing spouse is required so that the court, the trustee and creditors can evaluate the household's income.  This, however, in no way obligates your spouse, either legally or financially. 

Note:  If you both need to file, then you can wait until you are married; spouses that file together save on filing fees and other costs.