How do I toggle grayscale in Android 11?
Actually you can schedule and customize the Bedtime mode.
If you long press the Bedtime mode tile, it'll open the Bedtime mode screen.


In the schedule option, select all the days and in the time select 00.00 to 23.59, so as to keep it on almost the whole day(max. possible time - 23hrs 59 mins a day).
If you tap the Customize option, you can see a way to turn off the DND mode.

That's it, done! Now you can simply tap the Bedtime tile and it'll remain on
Once you've done this, you need not turn off DNS, while enabling Bedtime mode, as it's customized now.

A small point: Bedtime mode turns off an hour before if you've set an alarm, say you set an alarm at 5.00 a.m. Then, the screen turns back colorful at 4.00 a.m. And if you set an alarm daily at that time, schedule bedtime from say, 5.05 to 5.04 or so