I play Dota 2 mostly now adays, but recently been playing a bit of LoL again with my friends cuz I missed Ryze. He's a pretty big part of how I got to 1600 in Season 1.
Ryze will want as many early blue buffs as convenient, but is not dependent on them. Not getting a blue buff is never grounds for QQ on Ryze, cuz he plays fine without it. Obviously he's amazing with capped CDR and will want blue buff until he has his glacial. Usually this shouldn't be past the 3rd spawn. 4th if you are doing badly or need to rush a Negatron Cloak, which happens often enough.
In general 1st blue goes to jungler. 2nd one is great on him, but sometimes can't be spared and that's OK. 3rd one allows him to rush catalyst before glacial, which does wonders for Ryze, so try to at least get this one. Anything past that is emergency/luxury. Make sure you don't ever buy RoA. It slows Ryze down from items he needs way too much, and is weaker than many other choices in the late game when he has his core finished. Basically those who are suffering because they can't always have blue on Ryze are people buyin RoA, don't be one of them.
Blue is never absolutely necessary on Ryze. At 20% CDR he can still throw QWEQ combo with great effect. Also, for a mere 250 gold you can get an additional 10% for 2 and half minutes with an elixir. Great if you don't have full masteries yet. Also the mana regen isn't a high priority. You don't need to spam as soon as you get your tear, do some reasonable mana conservation early on. You'll max out tear regardless. Hope that helps.