Short Answer:
Yes! You can use guitar effect pedals on a bass guitar. Using effect pedals made for electric guitars with bass guitars will not damage your pedals.
Many pedal brands make bass-forward models of their pedals to perform best with bass guitars. Non-bass effect pedals will, at worst, not sound their best on a bass guitar due to their design.
Long Answer:
Today, we have plenty of types of effect pedal made specifically for bass guitars. These pedals are normally defined as such with pedals like the Electro-Harmonix Deluxe Bass Big Muff Pi 2 Fuzz Effect Pedal or the EarthQuaker Devices Blumes Low Signal Shredder Bass Overdrive. Pedals designed for bass are designed to best play with the normal frequency ranges electric bass pickups naturally put out – which are different from the normal frequency range output by your average electric guitar.
Your average bass-forward effect pedals usually include overdrives, distortions, fuzzes, and modulations. Bass pedals like the MXR Bass Distortion or Electronic Audio Experiments Greathammer Bass Overdrive are specially designed to accommodate the low-end frequencies of bass guitars with extra features like wet effect mix controls for performing their best on stage.
