My character is primarily a magic user and will use destruction spells as a means for combat. This is fine most of the time, but I've run into a couple bosses that have either absorb or reflect, I believe it's absorb, it's just turns purple and doesn't damage them. It's not 100%, but is annoying it being a chance to hit them or not. Is my best option to pick up conjuration and summon some mean monsters, or learn to use a blade or bow? Both?

It all depends on how you want to play. I always found it fun just to spam destruction spells. However, if you're looking for a 100% effective way to do damage, pick up conjuration and learn to conjure a sword. The additional benefit is that you can always summon a meat-shield if need be

The dangerous ones are the ones that Reflect. Your resistances won't stop your own magic reflected back on you, so you can actually kill yourself if you use a large enough destruction spell.

One trick that works is to create custom spells that combine Dispel on Self with your Destruction magic. This only works with Touch spells, but it completely prevents being damaged by your own magic, as long as the Dispel is high enough to match the Destruction amount (It's a 5:1 ratio; one point of Dispel will offset 5 points of magical damage.)

Conjuration is effective if you use the right summons for the job. Clannfears are the best for "seek and destroy" because they're fast and aggressive. Caster-summons like scamps and atronachs tend to back up while fighting, so they may actually draw an enemy to you. Zombies are tough, and they can stand up to multiple enemies for a while. In any case, if you use a summon, you have to learn to let the summon engage the enemy first, and take their aggression; otherwise the enemy will just ignore your summon and come after you anyway.

Ah yes. I forgot about the fire-and-forget effect of clannfears; always useful in a pinch

I agree with Conjuration.
However I use Turn Undead first. Then I make my summons. Then I leave. Let baby Clannfear do the rest. Then I come back and proceed as usual. Really for me, the only threat of having a spell come back at me comes from the undead, especially liches. So I turn 'em first if I can. If I miss, well.... guess I will have to take my chances with spell selection.