What is the structure of [Co(NH3)5SO4]+?
There's a certain amount of misinformation here:


  sulfate is a bidentate ligand


Sulfate is actually a flexidentate ligand, which is a term used to describe a polydentate ligand which is found to show different denticity in different complexes. Sulfate can act both as mono- or a bidentate ligand. Remember, just because it has two donor atoms doesn't make it a bidentate ligand. 

The occurrence of complexes where sulfate acts as a bidentate ring would also be rare owing to the fact that four-membered rings are strained. This page lists $\ce{[Pt(SO4)(P(C6H5)3)2]}$ as one example of such an occurrence.


  coordination number of cobalt would become 7. How is this possible?


If this implies that coordination numbers of 7 aren't possible, it isn't true. Coordination numbers of 3, 5, 7, 8-12, 14 are possible, albeit such compounds are quite rare. See this Wikipedia page for some examples.



Thus, the structure of the complex $\ce{[Co(NH3)5SO4]+}$ should be octahedral with cobalt showing a coordination number of 6.