Short answer: Yes.
The wizard waving his staff around and having magic arc out of the tip is classic fantasy, and using a ritual knife in one hand (an athame) is common in ritual magic. You just gesture with the blade instead of your fingers.
Now the ritual choreography with a bow may get a bit wonky to visualize, but if a wizard loves his bow so much he's bonded it in an arcane manner, he probably knows how to do it.
However, a weapon is generally a bad choice for a bonded object since there are lots of places you will not be allowed to take an obvious weapon, let alone wave it around in a threatening manner without attracting the attention of the city watch.
Officially you will need 2 hands to wield a bow.
However, the Arcane Bond ability says the bond must be "in hand", not that it must be weilded as a weapon.
If you can hold a bow in one hand, you can use it as an arcane bond in one hand. Using it as a weapon then requires the other hand.
Clear enough?
Is someone actually arguing the other way on this? If so, send them here, by the rules, they have no leg to stand on.
Kevin....
I completely agree with you as far as iconic imagery and thematic intent and RAI. What I'm curious about is there anything in RAW to indicate this?
I believe the RAW for this is the spellwurm from Magic of Eberron and the good old spirit naga: You do not, repeat, do not, need fingers or even hands to make Somatic components for spells. Wiggling a tail or even writhing your body is apparently more than sufficient, despite the fact that the RAW says you need to have a "hand" free.
Spirit Nagas don't have hands, so it's kind of hard to have them free with which to make the various sacred mudhras and assorted arcane hand gestures a mage would usually make with his hands. It would be rather silly to limit them to only cast spells which do not have somatic components or require them to take Still Spell for everything.
Spellwurms operate the same way, as sorcerers, despite having no hands, until they attach themselves like a leech in place of a missing arm or underneath a present arm, and they are able to then work as a substitute arm for spellcasting despite the fact that the tip of their tail has no actual hand at the end of it either.
Add to that evidence the Hypnotic Pattern spell, which in the current Pathfinder text requires as a material component either a stick of incense or a crystal rod, though doesn't mention what the hell you're expected to do with the damn things. However, in 1st edition, the text was more explicit: the stick of incense was lit or the crystal rod filled with phosphorescent material and the illusionist casting the spell created they hypnotic pattern by gesturing appropriately with the glowy thing.
Yes, this contradicts the current RAW on page 213 Pathfinder which says "hand" twice, but since the Pathfinder Bestiary also included the Spirit Naga with rather obviously has no hands and yet still somehow manages to cast spells, it's fairly obvious that they're using the word "hand" in the main book because it's assumed you're playing a humanoid spellcaster and it takes up less space than saying "appendage capable of fine motor functions." The verbiage on p. 213 that should be paid attention to is "a measured and precise movement" or the very 1st edition term "gesture."
You can gesture or make a measured and precise movement with a hand, a tail, a lit stick of incense, a knife, a staff, or even a large wooden spoon if that's what you currently have in hand. It may look a bit undignified to curse someone with a kitchen implement, but it should certainly work. I can also imagine a Tianese sorceress using a fan to the same effect.
So, in sum, while this may be RAI rather than RAW if you go with an overly literal interpretation of the RAW, the overly literal interpretation doesn't work because it's impossible to square literal "hand" with the obviously handless spirit naga which nevertheless still casts spells. And the spellwurm breaks this even further if you're accepting 3.5 RAW.
And as Hypnotic Pattern shows, we're playing a game where over twenty years of transcription and reinterpretation have left some things less clear, such as what's supposed to be inside the crystal rod and what you're supposed to do with the glow stick.