She handed me the basket and said, since someone might be watching, why not wait until I got home to open it.

Literal

She [topic-は] basket [object-を] me [to-に] hand-over, somebody [subject-が] is-watching [if/and-と] would-be-bad [because-から], home [to-に] arrive-back [until-まで] open-the-act [object-を] wait-do [how about-たらどうか] [quotative-と] said.

A long sentence stitched together with the chain conjunctive 手渡し (the renyōkei or i-stem of 手渡す), which lets one clause flow into the next without a full stop — a slightly more literary alternative to the everyday te-form 手渡して. Inside the reported speech, ~ているといけない frames a worry ('it would be bad if someone is watching'), and ~たらどうか literally asks 'how would it be if you waited?' — Japanese politely floats a suggestion as a hypothetical question rather than commanding directly. Note that the speaker's request never gets quoted directly: と言った reports it as a paraphrase, which is far more common in Japanese narrative than the verbatim '「…」' + と speech you might expect from English novels. The whole sentence has the air of a clandestine handoff — perhaps a love letter or small gift wrapped in a napkin.