Frellesvig [A history of the Japanese language] does not say very much about polite language, but here are some relevant bits:
Politeness is a prominent feature of cNJ [= contemporary modern Japanese] where polite style is expressed by the auxiliary -(i)mas- or the polite copula des-, but as with exaltation, there are NJ [= modern Japanese] dialects which do not have polite style. The grammatical expression of polite style is a relatively late addition to the language: OJ [= Old Japanese] did not have it at all, and while there are incipient uses in EMJ [= early Middle Japanese], it was not thoroughly established until early LMJ [= late Middle Japanese]. [...]
[...], in early LMJ, paber- was in this function replaced by sauraw-, which in addition to being used as a suppletive polite equivalent of ar- came to be used as an auxiliary verb, that is, attaching to the infinitive of verbs to express polite style, e.g. mi-saurawabaya ‘see-POL.OPT; if only I could see’, which is an early example from the Heike monogatari (early thirteenth century). This development made possible the expression of polite style with all predicate types and established politeness as a grammatical category in the language. Sauraw- comes from early EMJ saburap- which is said to be a changed from of OJ samorap- ‘serve, be in attendance’, also reflected in the word samurai.
During LMJ -sauraw- was used as the general polite marker; it changed to -sɔɔraw- by regular sound change, but also gave a number of other more reduced shapes with irregular inflected forms, such as sɔɔ- which was both used on its own as the nonpast form and as a stem for attaching other morphemes: sɔɔta past, sɔɔnu negative. This divorced its polite-style marking function from its use as a lexical verb. Thus, sɔɔrɔɔ and its different variants might best be understood as an auxiliary, rather than as an auxiliary verb, but it should be noted that they continued to function as polite variants of ar- in all its functions, including combining with the copula gerund de to form polite copula forms, e.g. de sɔɔrɔɔ or de sɔɔ. The cNJ polite copula des- is by some scholars thought to descent from de sɔɔ. [...]
Finally, in the second half of LMJ, -(i)sɔɔrɔɔ was replaced as the general marker of polite style by the auxiliary -(i)marase-, which is the source of the present-day polite style auxiliary -(i)mas-, e.g. from Esopo: i-marasuru exist-POL.NONPST ‘is’, osie-marasyoozu teach-POL.INT ‘(I) will teach’. As opposed to the other polite style verbs and auxiliaries mentioned above, -(i)marase- does not originate in a suppletive respectful or humble existential verb. Its OJ source is the humble verb mawir- ‘come.HUM, go.HUM’ (which itself is reconstructible as *maw + ir- ‘humble prefix + enter’), through lexicalization of the causative mawira-se- to a suppletive humble verb mairase-, which came to be used as a humble auxiliary verb -mairase-, which in turn in late LMJ was further reduced phonologically and became an auxiliary -(i)marase- which shifted from humble to polite, eventually being reduced even further to its present-day shape -(i)mas-; this is thought to have taken place early in NJ, but there are examples from LMJ which suggest that it may have happened already in late LMJ and that the two shapes -(i)marase- and -(i)mase- coexisted for some time during LMJ, but that the latter was only sporadically reflected in writing.
