I'm sorry to bring up an unpleasant topic during this dreary rainy season, but please bear with me for a moment.
Literal
Depressing rainy-season [to-に], refreshing-not talk [with-で] humbly-sorry [copula-ですが], little while companion-please [polite-ください].
うっとうしい 'gloomy / depressing / oppressive' describes the rainy season's atmosphere. 恐縮ですが 'I'm sorry / I humbly apologize (but)' is a very polite set phrase for imposing on someone. お付き合いください 'please accompany/bear with me' is a polite request formula. A classic polite-formal opening to an unpleasant announcement.