Are there any restrictions or advice on who should know about bonds in a Dungeon World game (RAW or in the spirit of the game)? Are they supposed to be public knowledge to the party? Between the two players (& GM)? Private to the player that wrote them?
Bonds are normally public. Step 12 of Character Creation (Dungeon World, p. 54) makes that clear. The previous step required everyone to introduce and describe their characters; this one says:
Take some time to discuss the bonds and let the GM ask questions about them as they come up. You’ll want to go back and forth and make sure everyone is happy and comfortable with how the bonds have come out. Leave space to discover what each one might mean in play, too: don’t pre-determine everything at the start. Once everyone’s filled in their bonds read them out to the group. When a move has you roll+Bond you’ll count the number of bonds you have with the character in question and add that to the roll.
Now, extending the game with hidden bonds might well be interesting, but I'd suggest you get the hang of using public ones first. In any case, you'll need to tell the GM about any hidden bonds, so that they can take account of them when the fiction demands that they have an effect.
The End of Session move requires you to look at your bonds, among several other things. If you have "resolved" a bond (by exploring everything that it implies, making it irrelevant, or otherwise completed its effects on the story) and the player of the character you have the bond with agrees that it's resolved, you take an experience point, delete the bond, and take a new one. Again, this implies that bonds are public. You could keep them secret, but they are revealed when you attempt to resolve them.
Thanks to the commentators for pointing out that there's a common convention for playing Powered by the Apocalypse games of having everything in the open, so that players can make use of everything in their contributions to the story. Of course, that doesn't mean the characters know everything about each other.