When it comes to bows, only two enchant methods work - Cast when Used and Constant Effect.
Constant Effect works all the time, and it is used to place positive effects on your character when wearing it. Ineffective in the context of your Soul Trap.
However, Cast when Used works when you use the bow like a scroll, generic item, not a weapon. For example if you have a Soul Trap Target effect and you want to use it from your bow, you have to choose the bow from the MAGIC menu, ready your "spell hands" and use it (unless you are using MCP Oblviion casting option).
I presume you were trying to achieve an effect that would work once you hit something with an arrow from the bow. (Like it is in Oblivion and Skyrim). However there is no possibility to do that in Morrowind. If you want your enemies to be affected when hit from the bow, you need to have the desired enchantment on the arrows. There are many available, but I doubt there are any with soul trap effect. If you do use the aforementioned MCP you can enable the option to enchant arrows - that way you could create soul-trapping missles.
Any weapon can harm any high level creature, unless it is a creature with "Resist Normal Weapons" effect. If that's the case, then it would depend on the ammunition you use. To harm such a creature with an unenchanted bow you'd need to use silver or higher-tiered arrows OR magical arrows.
Coincidentally, the one that this topic is about is the enchantment I use. "Cast When Used - Soul Trap 30 seconds on Target" It is convenient in that you don't waste charges on creatures you don't want to soul trap or NPCs or on subsequent attacks on the same target (as it is cast independently of attacks).
Another enchantment you could use would be fortifying attack, marksman skill (all to increase hit chance), strength (for damage) or even any magical damage, so that you can cast spells from the weapon.