The way to combat bow spamming is to get a bow first and eliminate everyone before they get a bow :p
For real though, to combat bow spamming it takes a great deal of parkour skill along with a bit of luck. The one thing you simply cannot do against a bow spammer is attack him straight from the front. For instance, he shoots you with a bow, you run straight at him without moving left or right. This is a for sure death against bow spammers. Also, try to find a corner to "hide" where they cannot shoot you off from. Once they leave to get tnt/stronger bow, you can make a run for either mid or another island.
If you are not good with running away, you can always try a shield. However, if you are near the edge, using a shield is almost a sure death. For those of you who do not know, shields prevent arrow knockback. However, it does prevent melee knockback. If you are on the other end of this, the way to kill them is to bow spam them with your punch bow, then when you are right next to them, hit them with a melee attack from the bow then quickly shoot an arrow. Most of the time after attacking them with melee they will take down their shield and the arrow you fire will knock them off :)
Let me know if this post helped you :)
(Also I just got home after working 11 hours so if there is any grammar errors I apologize)