Landlords in Michigan, and in most other states, have a duty to provide a "habitable" premises for their tenants. This is commonly called the "implied warranty of habitability."
An apartment that is infested with bedbugs may be considered a violation of this requirement, and the landlord would have a duty to remedy the infestation. If however, after they have been a notified and given a reasonable time to fix the problem the tenant has some additional options. One option is to not pay rent until the problem is solved. The second option is to pay to have the bedbugs taken care of and to deduct the costs from the rent that you pay. For both of these options there is the possibility will attempt to evict the tenant from the premises and the tenant would raise the bedbugs as a defense in the eviction action. In either case the tenant should put the withheld rent into a separate savings account and not spend it. This shows the judge in an eviction action that you aren't just trying to get out of paying your rent.
The final option is to leave the premises. The violation of the warranty of habitability would provide a defense against a suit by the landlord for the remainder of the rent that would have been due for the remaining term of the lease.
It sounds like you have notified the landlord of the issue; if you haven't done so in writing it would be prudent to do so. Below you can find two links from the state of Michigan and Michigan Legal Aid that may help you.
The question relly is : Can you successfully sue the Landlord?
Of course you can sue as you are in privity of contract under the lease. The question for the trier of fact is : Were the bugs in place prior to your occupation or post occupation?