We measured spectral noise density in YBCO symmetric bicrystal Josephson junctions on sapphire substrates at bias voltages up to 100 mV and T 4.2 K. Normal state resistance of the Josephson junctions, R-N = 20-90 Omega and ICRN up to 2.2 mV have been observed in the experimental samples. Noise measurements were carried out within frequency bands of 1-2 GHz and 0.3-300 kHz. At bias voltages 10 less than or equal to V less than or equal to 60 mV a linear voltage dependence of noise power has been registered, while at V less than or equal to 5 mV a noticeable noise rise has been observed. The latter may explain the experimentally measured linewidth broadening of Josephson oscillations at mm and submm wave frequencies in high-Tc superconducting junctions. Experimental results are discussed in terms of bound states existing at surfaces of d-wave superconducting electrodes.