For a character with a military background and proficiency in modern firearms, would any additional training be necessary for them to master a crossbow? If so, what kind?
For actual training? Not much. They’d need to be run through how to reload, and maintain the weapon. If they were a fairly quick study, that should only take a couple hours. Mastering the weapon would require lots of practice.
The problem is, the crossbow fires a much slower, heavier, projectile. This doesn’t invalidate basic concepts of how to aim and fire, but it does change the parameters where the weapon will be effective. Drop will be far more severe, meaning they’ll need to compensate for that, and the overall range will be much more limited (roughly 50 – 60 meters.)
In order to do that, they’ll simply need to spend time on a range practicing and gathering data on how the weapon performs.
When shooting, it’s very important to collect Data on Previous Engagements (or DOPE) for that weapon. This primarily involves learning how that individual weapon behaves at various ranges. (So, your character would be learning how their rifle or crossbow behaves, not necessarily all rifles and crossbows.) Some will keep DOPE as physical records, others will simply internalize the information based on how the weapon handles. You can collect some of this information online, but ultimately you need to confirm it with the actual weapon before you can count on it.
The end result is, they can probably swap over to a crossbow with a minimum of effort, but they would need to spend time on the range getting a feel for how the weapon handled, particularly in relation to compensating for bolt drop.
Drop is a concept in shooting involving the projectile as a physical object. While it is traveling away from you at high speed (~400 feet per second with a crossbow bolt) it is also falling. Gravity does not give bullets, bolts, or arrows, a pass simply because they’re already going in one direction. This is referred to as, “drop.” When aiming you need to account for this. Drop can be compensated by either zeroing the sights/optics for a specific range, or manually by the shooter.
For example, a shooter who zeroes their scope for 100 meters, will need to aim below the target at closer ranges, and above the target at ranges exceeding that range. To the point that at ranges over 500m the shooter may be aiming several feet above the target.
Factors like relative elevation can further affect calculating drop, with targets above the shooter requiring them to overcompensate for distance, and under-compensate for targets below them.
Another major factor is wind, which can affect a bullet, and may require the shooter to adjust their drop expectations, as well as left to right drift. (If the bullet has a backwind, it will travel faster, and as a result, will reach it’s target sooner, requiring less drop compensation. A headwind will slow the bullet, increasing the effect of drop. Crosswinds will require assessing the speed, and adjusting the aim point to compensate.)
Because the bolt is larger, and slower, all of these factors will be far more pronounced than with a bullet. Meaning a prospective crossbow user will need to collect new DOPE for that weapon. The rough values can be extrapolated from math that can be calculated from available data (the speed of the bolt, its mass, distance to target, ect), but that will only provide a starting point, it won’t be sufficient to really, “master” the crossbow. For that, your character’s simply needs to spend some time practicing, and getting a feel for their weapon.
Incidentally, all of this is also true for a character picking up a new gun. Those will be similar to comparable weapons, but even then, getting highly precise shots off requires spending time with that, specific, firearm. Practicing, and getting a feel for it. Now, with practice on a wider variety of firearms, collecting DOPE for new guns will become faster and more intuitive, but it’s still something your character would need to do.