Is my battery safe from over discharge?

I didn’t find a specific answer to this. I know the BMS is there to make sure the pack charges safely, but does the BMS also mean the battery pack is safe from damage due to being discharged too far? I ran the battery low enough yesterday that the bikes controller, which also has a low voltage cut-off, shut down power if I gave it too much throttle. Is that OK since the pack has the BMS?

Don't we need a link to the BMS and battery to answer?

Some are adjustable.

For LFP for example I would not allow below 2.9V, maybe 2.8V for higher C rates.

For House loads, 3V.

You should set your bike's controller to shut down before you overdischarge your battery. Don't rely only on the BMS.

yes with a bms the battery is safe. The bms usually shuts off when one of the cells reaches its over discharge limit. The bike controller monitors overall voltage and will usually activate before the bms. Your battery will be ok.
But if possible you might want to add a voltage monitor to see the battery voltage in real time. Thats just so you never have to wonder whats going on with the battery.