Congrats on your find--commercial 1903s with good bores aren't exactly easy to find nowadays. Usually the underside of the bolt handle has a serial stamp, although I've seen several that were mis-marked, always just a number or two off what appears on the rest of the gun--I think it must have been a relatively common (or at least not-unheard-of) assembly gaffe in the factory. Given that, a bolt with no number whatever seems perfectly likely. Does the script on the action ring read "Made in Austria," in English? If so, it probably would have been an export gun to Britain or America. Griffin and Howe and Sequoia Importing Company literature from the '20s advertise both single and double-set triggers, though the latter seems to be much more common. Regarding barrel length, the above quoted 17.7" was standard, although factory variations do exist--these rifles had a terrific amount of handwork, and special-order lengths and features could certainly be had. I would guess that custom features occur more on European-market guns than the English-script export guns, though I don't know this for sure. If you intend to hand-load for your 1903, I and I'm sure others on here can give you some pointers--the gun/cartridge combo is a bit more complicated to load for than most, though a lot of fun once you iron out the kinks.
Best,
Malcolm