Applying for an MBA after your business has gone bankrupt does not have to be a weakness. Business schools appreciate innovation and entrepreneurship. The experience of starting and running your own company can be an interesting perspective you can bring to enrich the MBA program. Even the lessons learned from the failed venture can be worthwhile as well. There are some key questions on the minds of the admission boards when evaluating an entrepreneur whose business has failed.
First, they will evaluate the scope of the business (is this someone tinkering with a hobby or is this a real venture?) Then they will assess what you achieved (did you create a product that is being patented/raise funds from investors to expand the business or did the business not take off in the first place?) And finally, they will investigate why the business failed and the lessons you learned from the bankruptcy (are there holes in your skill set that you need to strengthen or did you make glaring mistakes that raise questions about your judgment?)