We have investigated the mode-changing properties of PSR B0329+54 using 31 epochs of simultaneous 13 cm/3 cm single-pulse observations obtained with Shanghai Tian Ma 65 m telescope. The pulsar was found in the abnormal emission mode 17 times, accounting for ~13% of the 41.6 hours total observation time. Single pulse analyses indicate that mode changes took place simultaneously at 13 cm/3 cm within a few rotational periods. We detected occasional bright and narrow pulses whose peak flux densities were 10 times higher than that of the integrated profile in both bands. At 3 cm, about 0.66% and 0.27% of single pulses were bright in the normal mode and abnormal mode respectively, but at 13 cm the occurrence rate was only about 0.007%. We divided the pulsar radiation window into three components (C1, C2 and C3) corresponding to the main peaks of the integrated profile. The bright pulses preferentially occurred at pulse phases corresponding to the peaks of C2 and C3. Fluctuation spectra showed that C2 had excess red noise in the normal mode, but broad quasi-periodic features with central frequencies around 0.12 cycles/period in the abnormal mode. At 3 cm, C3 had a stronger quasi-periodic modulation centered around 0.06 cycles/period in the abnormal mode. Although there were some asymmetries in the two-dimensional fluctuation spectra, we found no clear evidence for systematic subpulse drifting. Consistent with previous low-frequency observations, we found a very low nulling probability for B0329+54 with upper limits of 0.13% and 1.68% at 13 cm/3 cm respectively.