Bogdanowicz, Stefan Rudiszcza,[Minsk] Russia 24 1887 1911
Bachdanowicz, Jozef Rudice, Russia 21 1889 1910
Is it possible the above 2 males are related to your ancestor?

Bogdanowitz, Anna Ruditzy, Russia 3 1910 1913
Bogdanowitz, Iwan Ruditzy, Russia 32 1881 1913
Bogdanowitz, Maria Ruditzy, Russia 34 1879 1913
Bogdanowitz, Maria Ruditzy, Russia 1 1912 1913

Iwan and Maria were naturalized citizen - set of numbers and a date by their name on the NY EI arrival manifest. Have you requested their intent and petition?

http://www.jewishgen.org/communities/loctown.asp
Ruditsy populated place 54°07' N 30°44' E E M U G Belarus 129.6 miles E of Minsk 53°54' N 27°34' E

Ruditsy, Рудицы populated place 56°01' N 29°31' E E M U G Russia 313.8 miles W of Moskva 55°45' N 37°37' E

distribution of BOGDANOWICZ surname holders in Poland:
http://www.moikrewni.pl/mapa/kompletny/bogdanowicz.html