Hi,

should you not find what you're looking for, I'd encourage you to experiment yourself with bxfr, starting from a sound and changing parameters one by one from minimum to maximum value (mind your ears! always keep volume at safe levels! :) ) and learning by ear how they affect the sound. In its relative simplicity, bxfr exposes concepts you'd find on more complex and powerful synths, so it could be a good way to introduce yourself to sound synthesis.

I'd also suggest at least some glossary-like short reading about some common terms, like this one on the envelope:

https://en.wikipedia.org/wiki/Synthesizer#ADSR_envelope

Of course, the more you'll feel like reading, the better :)

Incidentally, a sound similar to what you're looking for has been recently posted on Freesound, all synthesis and no samples:

http://www.freesound.org/people/zimbot/sounds/231903/

It's been done with Analog Box.

You're welcome :)

You picked a very tough nut to crack, the sound I linked was done inspired by a thread where the requester was looking for a realistic rendition of it, and even by working with samples that weren't exactly the right source would hardly get near enough.

Now, since you wisely want consistency along all the sounds for your project, I guess you can do with less realism, but I see your concern with laser-like "pew" sounds not being proper.

Anyway you might have to overlay different sounds, like it's been done with samples in that thread, as there are actually more sounds together, like the snapping cord, eventually the slide of the arrow body against the bow and a hiss from air resistance. The problem with bxfr is that most of its generators are too "musical", easily leading to the futuristic sounds you mention, and the noise generators may sound too bit-crushed for a smooth hiss, even with bit crusher disabled.

Your best bet for making things sound less musical even with regular waveforms is a slightly negative "Frequency Slide"

This one is an example of a short noise with a few things possibly in the right direction, it might be a start:

http://www.bfxr.net/?s=5%2C0.5%2C%2C0.03%2C0.595%2C0.155%2C0.3%2C0.1%2C%...

EDIT:

 ...more drastically high-passed:

http://www.bfxr.net/?s=5%2C0.5%2C%2C0.03%2C0.595%2C0.155%2C0.3%2C0.1%2C%...

This could be the base for the hiss before the string snaps:

http://www.bfxr.net/?s=2%2C0.5%2C0.12%2C0.14%2C0.13%2C0.24%2C0.055%2C1%2...

I use the online SFX generator for many of my sound effects in my rpg game.  

Here's the List of sound effects that I used it SFX for.

Beep, alarm, bomb tick, boom explode, Repair, Spider Venom, corral in pen confirmed, click, Heal, Power Up, Reactor Core,  Radiation Beep Meter, Click on menu, Switch, Timeleft, teleport out, fall, thud  wasp - for one of the creatures in the game, computer sound, 1 Factory crusher sound effect and crush. Dimensional Creature Transport sound effect, droid, droid hit, give item, crawler sound effect, crawler crash, empty status, factorythump, Flanblast (jelly creature), hheal (enemy heals), lift select, lift up, lift down, jumped, killbo, (creature die), lift password code, machine 1, machine 2, access denied, nuclear alarm warning, outofstock, leak patch for radiation suit, droid patrolalert.wav, posion potion effect, posion left, probe sound effects, rift sound effect, roll sound effect for Guardian of the Lakes (BOSS),  Runestone Purchase sound effect from store, security bot beep, sleep1, spraygun, teleport in.

It's a very useful program.