From: https://core.telegram.org/bots/faq#broadcasting-to-users
Broadcasting to Users
My bot is hitting limits, how do I avoid this?
When sending messages inside a particular chat, avoid sending more than one message per second. We may allow short bursts that go over this limit, but eventually you'll begin receiving 429 errors.
If you're sending bulk notifications to multiple users, the API will not allow more than 30 messages per second or so. Consider spreading out notifications over large intervals of 8—12 hours for best results.
Also note that your bot will not be able to send more than 20 messages per minute to the same group.
How can I message all of my bot's subscribers at once?
Unfortunately, at this moment we don't have methods for sending bulk messages, e.g. notifications. We may add something along these lines in the future.
In order to avoid hitting our limits when sending out mass notifications, consider spreading them over longer intervals, e.g. 8-12 hours. The API will not allow bulk notifications to more than ~30 users per second, if you go over that, you'll start getting 429 errors.
See also: How to avoid hitting limits?