Bow progression can be done through the crafting table or the smithing tabe although by default only the smithing table option is available. This of course can be changed in the config.
Both methods behave near identicaly and as is probably obvios works as a progression:

half iron -> iron -> half diamond -> diamond -> netherite

At each stage you add one item of the material being progressed towards. iron ingots for iron diamonds for diamond etc. The one differece in this is when the crafting table option is enabled that there are recipes to skip the half state by adding two of the material instead of one.

and as you might have guessed already gold is in on its own being the only material in its progression:

half gold -> gold

Crossbow progression is simmilar to Bows except it doesn't have the half varients and it takes three items instead of one ore two. naturally the one exception is netherite which is still done with one ingot and in the smithing table unlike the rest that have to be done in the crafting table.