Supposedly is supposed plus -ly. On its own, supposed has two syllables, suh-POHZD, because the ed is just a d sound. But when -ly is added, the ed becomes a full syllable again: suh-POH-zid-lee.
Other -edly words do the same: allegedly is uh-LEJ-id-lee, markedly is MAR-kid-lee and deservedly is dih-ZUR-vid-lee. If you drop the extra syllable, the word sounds rushed and unclear.
Supposably is a real but rare word in some dictionaries, meaning as can be supposed. Most people who say it mean supposedly. In everyday English, use supposedly, with a d and no b.