Do not make too many quivers. Sometimes marksdwarves store their quiver loaded with combat ready ammunition in a finished good stockpile and seemingly all other ranged soldiers get so confused by the presence of that full quiver that they refuse to pick up new bolts (and consequently prevent archery practice).
Going through your finished goods bins and dumping the bolts in the quivers (not the quivers themselves) helps. Your best bet to stop this completely would be to only have the exact 1:1 ratio of quivers:marksdwarves. The 'bug' probably fixes itself after a couple of game months when said dwarf picks up the full quiver again, but thats valuable time between seiges wasted on not training.
As for bolts: yes, if you have magma forges going, just set one to bolts/R and produce training bolts with whatever abundant metals you have. A dwarf armed with masterwork steel bolts that doesnt hit anything is no better than a super-sharpshooter equipped with bone bolts. If given the supply they need, training dwarves can go through ammo really quickly.
Do not assign them too many bolts and dont fiddle with "wood bolts for training, steel for combat". Having a too complex equipment system can cause equipment mismatch errors, long response times and overall confusion or every dwarves favourite: all of them together.
Build fortifications. Force your marksdwarves into a position where they can see the enemy, but not path to it directly. Build archer towers or carve some fortifications that are only accessible through the baracks around your entrance area, a simple moat, etc. do whatever you need to do to keep them from pathing to the enemy.
Ultimately, you want your melees to spar while training. It is basically a toned down danger room - they will go through combat without any real danger to themselves. Dwarves with widely different skills do not spar (at least that is what I've found). DF is really close to reality in that regard as it doesnt make any sense to pit a totally unexperienced teenager into your veteran squad. They will try to teach him instead of sparring. Try to make several small well balanced squads and a maybe a rookie squad with a very competent and experienced teacher as a leader.
It will still take a long time to get kickass soldiers with only training, though. As already mentioned, setting up an arena where you can have controlled fights with captured prisoners skyrockets combat abilities in comparison to normal demonstrations.
Other than that if push comes to shove, only the strong or the lucky survive and come out on top with more experience... the others simply weren't good enough and will not hinder training any further.