Can you install a dryer outlet using the bare copper as a neutral wire in an older house?

Technically, yes you can. However, this is one of the most dangerous things you can do in electrical wiring. It's not only against the code, it's a fire waiting to happen. Don't do it! Understand, the neutral wire is a conductor. It carries current. It needs to be an insulated wire. Also, if you use the bare copper (ground) wire for a neutral, you have taken away the earth ground from the circuit, eliminating short circuit protection. If the dryer motor shorts out it will burn up. (fire again) A residential dryer requires a 30 amp 220 volt circuit breaker in your panel and a # 10 gauge wire with three conductors (insulated) and a bare ground. Have a qualified electrician install it.