I am self-studying on how 802.11b bandwidth and data rates are calculated, primarily those of 1 and 2 Mbps. These are my understandings, please correct them if they are wrong. Please keep in mind I am not an electrical engineer.
At 1 and 2 Mbps, DSSS performs signal spreading resulting with 11 and 22 mega bits (chips) per second for BPSK and QPSK, respectively. In both cases, this stream has to be modulated with mentioned modulations and equal symbol rates of 1 Mbaud per second.
Bandwith equals 2 times bits_per_second/number_of_bits_per_symbol (1 or 2 depending on modulation scheme). This "2" at the begining is because of null-to-null bandwidth of a modulated signal. For both cases, the bandwidth is 22 MHz.
The data rates are equal symbol_rates times bits_per_symbol, resulting with 1 and 2 Mbps.