This is a construction where usage has changed over time. A century ago, the preposition to would almost never be included in OP's example, but today it usually would be...
Having said that, I don't think many native speakers would consciously recognize the prepositionless form as "dated". I only just discovered this significant usage shift1 myself - because the question piqued my interest, and because it's now quite easy to investigate such matters using online corpora.
So it's probably better for OP to stick to #1 because it'll make him sound "more like a native speaker". But rather curiously, hardly any native speakers would notice anything "odd" if he used #2.
Note that syntactically you admit [to] something. The thing admitted [to] must be a noun (note that gerunds are "verb forms functioning as nouns"), so there's no role for an infinitive verb form here.
1 I've now realised the particular text I chose for my chart rather overstates the shift - but this and this both show even more clearly what a "recent and upcoming" usage the preposition represents.