Both sentences are correct but have different meanings. You do need to start both sentences with "The".
"The client's office is located near the bus station"
"The client office is located near the bus station"
The first sentence refers to a particular client. For instance, I have a client, "Microsoft" and I am going to visit their office. ie. I am going to visit my client's office.
In the second sentence, 'client' is in collocation with 'office'. Together 'client office' *generally* means an office that services your clients. For instance, I own a company and I have several clients. I need an office or outlet that services all my clients. This is my 'client office'.
BUT, people may occasionally mistakenly interchange the two ("client's office" and client office"). ie. In conversation they may say "client office" and mean "client's office". Something to be aware of.