There is no single word in Irish equivalent to English "will" (or "would").
"Beidh" does not mean "will"; it is the future tense of the verb "bí" ("tá") and means "will be".
"mbeidh" is the eclipsed form of "beidh", which is used after certain particles such as "an" (interrogative), "nach" (negative interrogative), etc.
To express the English "would" in Irish, you need to used the conditional tense of the verb.
e.g.
Bheinn = I would be
D'ólfainn = I would drink
D'íosfainn = I would eat
Cheannóinn = I would buy
Bheifeá = you would be
D'ólfá = you would drink
D'íosfá = you would eat
Cheannófá = you would buy
etc.