this command:

give @p minecraft:spider_spawn_egg{EntityTag:{Passengers:[{id:"skeleton",HandItems:[{id:"bow",Count:1}]}]}}

should give a spawnegg whch spawns a spider jokey
when summoned with the command

/summon minecraft:spider ~ ~ ~ {Passengers:[{id:"skeleton",HandItems:[{id:"bow",Count:1}]}]}

the summon command does work, so the formatting must be correct.
other tags used with spawneggs still work, the only exeption is the passengers tag