Is it permissible to say "Bismillah" before eating a meal that my friend bought for me?

Friendship between foreign men and women is not permissible due to the evils and indecencies that result from it. As for the ruling on a woman buying a meal for a man, it falls under the ruling of a gift, and the original ruling for a gift is permissibility, even between non-mahram individuals, provided certain conditions are met. If the relationship is forbidden, then the gift is unlawful and forbidden gain (suht muharram), but there is no harm in saying "Bismillah" (in the name of Allah) when eating it, because its prohibition is incidental.