Can I activate my "once per turn" effect twice if the activation is negated?
The answer is yes.

There is a difference between negating the activation and negating the effects of cards. "Only once per turn" effects, like "Spellbook of Secrets", may only be activated once per turn, and if the activation is negated you can use them again. However, if the effect is negated, say, with something like "Ash Blossom &amp; Joyous Spring", you have still activated the card, and you cannot activate another copy.

You can read more about the distinction among these mechanics here.