Record high 19.125Gb/s real-time end-to-end dual-band optical OFDM (OOFDM) transmission is experimentally demonstrated, for the first time, in a simple electro-absorption modulated laser (EML)-based 25km standard SMF system using intensity modulation and direct detection (IMDD). Adaptively modulated baseband (0-2GHz) and passband (6.125 ± 2GHz) OFDM RF sub-bands, supporting line rates of 10Gb/s and 9.125Gb/s respectively, are independently generated and detected with FPGA-based DSP clocked at only 100MHz and DACs/ADCs operating at sampling speeds as low as 4GS/s. The two OFDM sub-bands are electrically frequency-division-multiplexed (FDM) for intensity modulation of a single optical carrier by an EML. To maximize and balance the signal transmission performance of each sub-band, on-line adaptive features and on-line performance monitoring is fully exploited to optimize key OOFDM transceiver and system parameters, which includes subcarrier characteristics within each individual OFDM sub-band, total and relative sub-band power as well as EML operating conditions. The achieved 19.125Gb/s over 25km SMF OOFDM transmission system has an optical power budget of 13.5dB, and shows almost identical bit error rate (BER) performances for both the baseband and passband signals. In addition, experimental investigations also indicate that the maximum achievable transmission capacity of the present system is mainly determined by the EML frequency chirp-enhanced chromatic dispersion effect, and the passband BER performance is not affected by the two sub-band-induced intermixing effect, which, however, gives a 1.2dB optical power penalty to the baseband signal transmission.