Offset Quadrature Phase Shift Keying (OQPSK) like QPSK transmits two bits per symbol. However, because of the offset on the quadrature component there are two transitions per symbol. Does this not double the bandwidth of each symbol, leading OQPSK to be more similar to BPSK in terms of spectral efficiency? This would make it 1 bit/s per Hz?
The spectral efficiency is the same as QPSK.
Consider the I and Q streams separately. Each has a certain bandwidth $B$. Shifting or delaying the stream does not change its bandwidth. So, shifting one of the streams relative to the other does not affect the overall bandwidth.