Yes it's OK to put bleach in the sink to clean it or help clean the drains.
There's no problem with using bleach in the sink or other drains to help clean them and disinfect the sink and drains.
I run a little bleach in my sinks to clean them and it's okay and never has caused a problem.
Just don't pour too much bleach in the sink too often because I've heard that it can damage your plumbing system but in moderation the use of bleach in the sink and other drains is perfectly okay.
Also when using bleach make sure to have proper ventilation so that you don't breathe in the bleach fumes and never mix ammonia with bleach as that is very dangerous as it creates a dangerous and deadly gas.