By drawing the bow in this specific way, other players sometimes do not see your bow draw animation:

1. Hold down right click (or what your "use item" key is) for a second or two.
2. Use either the scroll wheel or number key to switch to the slot the bow is in.
3. Sometimes the bow will not appear t draw for other players. (but the sound still plays)

Demonstration with keyboard and mouse overlay is attached. The video was done on a vanilla LAN server in 21w20a.