The term bidding prayer has a confused history, given in OED at bidding, vbl. n., meaning 6 (much of which is quoted directly here, and all of which has been used). It is basically a label for certain kinds of prayer in services of the Church of England, but the meaning of the label can be disputed, and has certainly changed over time, mostly with changes in grammar.
"As to these expressions there has been a series of curious misapprehensions. The original meaning down to the Reformation [say 1530] was ‘praying of prayers,’ i.e. saying of prayers, praying ... [This is a kind of hidden possessive] [From early on], it was the custom to request the prayers of the faithful in behalf of certain persons and things; and in the 16th c[entury], in England, [the rulers of the church used to order their congregations whom, or what, to pray for]. As bid in the sense of ‘pray’ was now becoming obsolete, ... bid [was] taken in the sense of ‘order, direct,’ so that [by 1600] the ‘bidding of prayers’ was [taken as if it meant 'the ordering or commanding of] prayers.’" [This too is a hidden possessive]. With the later use of the verbal noun as a gerund directly governing an object" [in other words, the 'bidding' came to be understood as an action being done to 'prayers'] "we have in the 17th c. ‘the form of bidding prayers’ or ‘prayer’ (= precationem hortandi [the Latin means 'asking [for] prayers [to be said]']); and later still, a misunderstanding of the grammatical construction in this phrase has given rise to the vulgar error of calling this exhortation to the people (in which ‘concionatores populum hortabuntur ut secum in precibus concurrat’ [Latin: 'the leaders urge the people to assemble with them in their prayers']) ... ‘the bidding-prayer,’ as if it were itself a kind of prayer qualified by the attribute ‘bidding.’"