" dumpling " is just a general term of almost any kind of 餃子. " Pork dumplings " or " pork dumplings in soup " could be 水餃 too. I think you may say " steamed pork dumplings in Shanghaiese style " to describe 小籠包. PS.: I won't remend to use " bun "
since bun is kind of bread
which 小籠包 is not a kind of bread.
小籠包英文是 Steamed pork dumpling. 臺灣有名的鼎泰豐小籠包就用這個英文名。
參考: 鼎泰豐homepage
小籠包英文系Steamed Pork Dumplings
參考: 自己