Ryze is literally one of nasus's easiest matchups. He will go oom trying to damage you, then when he has no mana left, you just continue farming like hes not even there.
On top of which, he has no mobility aside from the ms boost on his ult, which is largely irrelevant because if your jungler ganks, a wither to the face is the first thing ryze is gonna get, negating most of the additionnal movement speed, and resulting in a dead ryze most of the time, or at the very least a blown flash.
Ryze is pretty much never getting ignite, which is perfect for you.
If he isnt even abusing his range by autoing every single time you try to last hit a minion, it gets even easier.
Honestly, im thinking your runes/masteries or build must have been horribly wrong in that game. Here is what i use.
Masteries : 4/26, taking sorcery for the 5% cdr to complement 5% cdr from runes (quints) taking as much mr from the defensive tree as possible ( i have a dedicated anti-ap mastery page)
Runes : marks can be whatever you want, armor seals (because autos) and mr glyphs. Against ap tops i have a runepage with 2 cdr quints and an mr quint
Build order : against ap toplaners, you want to rush negatron cloak and spectral cowl before you get any cdr items. The problem with kindlegem is it wont provide any defensive stats. Once you have spectral cowl, ryze wont be doing much damage to you and you can just get cdr.
As for starting items, i favor doran's shield against ranged champs, and ryze is no exception. Flask is also very good at sustaining if you dont feel comfortable with only one pot. Null-magic mantle would be ideal against any ap who cant get autos off (think melee champs like cho'gath, akali, etc.).
Past a certain point (levels 9-11, with decent stacks), ryze is just dog food. yes ryze scales decenttly, but it doesnt compare to a nasus who has been farming more or less freely for most of the laning phase. I personnally havent lost lane against ryze in a long time.