There's not really one single way to solo on SMN, but the most important thing to understand is hate mechanics. Summoners roll with very low hate. We have to in order for a fresh avatar to get hate off us. The thing that distinguishes a good SMN from a bad one in solo or pet-burn type scenarios is often their management of enmity.
That being said, a few important things to know:
1. Enmity generation occurs based on how close your target is to anything that your spell/ability might build enmity on. The maximum range is roughly 30 yalms for most monsters (some NMs seem to have extended ranges but it's very rare). What this means is that, say for example you are 15 yalms from the monster your avatar is fighting and you cast Stoneskin. This will generate enmity. Now say you're 35 yalms away and cast Stoneskin, no enmity. Here's where it can get tricky... let's say you are 35 yalms away, but your friend is 15 yalms away and you Cure III your friend. This will generate enmity because even though you're far enough away, they are not. It's the target that matters.
How does this apply to SMN solo? Well for one thing, when you run away to resummon your avatar, you need to FINISH casting your summon before the monster gets within about 30 yalms from you. If you can do this, you will generate no new enmity. If you do this consistently, your avatar will have no trouble pulling hate from you in the first swing, even if the swing is a miss! Secondly, it's important to run away before curing yourself or casting Stoneskin. Don't stand just out of AOE range and start buffing yourself or you will generate enmity. If you build up too much enmity, you will have a very hard time keeping hate on your avatar which, as you discovered, is key to SMN soloing.
That being said, there's really two key ways to solo on SMN:
1. Hate-free kite. Basically you just summon & run away. Wait for avatar to die, repeat. Very simple. Absolutely essential to keep enmity at or close to zero for this. One mis-summon (spell finishes too late) can make it hard for the avatar to pull hate off you for the next 4 or 5 resummons. Carby is often used for this, but if you can get other avatars for free they work better. Fenrir works the best as he attacks faster than other avatars and does the same damage.
2. BP kiting. Basically same as hate-free kite, except that every time you resummon, when the monster approaches, you BP it to do damage and stick hate to your avatar again. Then you run away and wait for it to die, or release it when your BP timer is almost up. This can be risky because using a Blood Pact generates hate on the BP's target, and it's not an insignificant amount of hate. This is counter to the SMN goal of minimal enmity. However, it can speed up the battle by several orders of magnitude. This is the preferred way to solo, if it can be safely accomplished. The other way, as you discovered, is dreadfully slow. A really good tip for this method is to Assault after you BP. Many people Assault before BP but the BP locks their avatar in place and Assault has a 10-second cooldown. BP first (when the monster is about 15-20 yalms away), then Assault after and your avatar won't stand there looking dumb while they ready their BP.
____________________________Pergatory (Asura, Kupo LS) WHM99 ~ SMN99 ~ DRK99 "If you want to know me, look inside your heart." -Lao Tzu