If I understand the logic behind your question, you are asking:
Since movies is plural, why is the singular movie and not movy?
In general:
Well, just because there is a common and helpful rule that states
A noun ending in a consonant and then y makes the plural by dropping the y and adding -ies
this does not mean that you can always apply this rule backwards to any plural word ending in -ies to get the singular of that word.
That is, there is no rule that says a word whose plural form ends in -ies comes from a singular form that ends in consonant plus -y.
You can apply the rule backwards, when it was originally to a word, as in
daisies : daisy
ponies : pony
But you cannot apply the rule backwards when it was not originally applied. Thus the following does not work
monies : mony
(Note that money has two plural forms, moneys and monies.)
In Particular
And the following does not work:
movies : movy
Because the singular of movies is not movy but movie. The why of that has to do with movie coming from moving picture. Mov(ing picture).
The -ing picture was replaced by the ending -ie. I suppose it could have been replaced by y (after all, we have such nouns as gravy.
I suspect that movie(s) originally had a diminutive meaning, in which case the ending -y seems to be fine only in words whose last consonant is doubled (doggy, granny) while -ie goes with those kind of words (doggie, grannie) or...
with words whose consonants are not doubled (sweetie, birdie). I guess movvy didn't quite work, any more than movy.
A similar word to movie, now outdated, is
talkie
It has the plural talkies. The word talkie apparently does not come directly from talking pictures, but from movies. The mov- was replaced by talk-.
Note that we have 'walkie-talkie'. This conforms with -ie usage in words whose ending consonant does not double. But later on came the form 'walky-talky'. One can only guess why this variant spelling came about.
I think this is a trivial matter in the sense that no one will fault you if you spell it bi-monthly or bimonthly. Anyway, the entry is under bimonthly at dictionary.com and Merriam-Webster bimonthly. The examples given at dictionary.com are from works that are at least one hundred years old. If we look at some search results, we see that bimonthly is more popular.
So all in all, I would write bimonthly.
Best Answer
Because so-called long vowels (a, e, i, o, and u, when pronounced "like their letter name") and digraphs do not require a doubled consonant to form the participle.
Compare hating or waiting with batting, for example. Or plan and plane, which become, respectively, planning and planing.