Is it correct to say “Me basta con que escribeme una vez al mes”? Given there's a que before the verb, shouldn't it be written in the present subjuntive (escríbame)?
Also, is con appropriate in this case?
The correct form for the sentence, if the intended meaning is "It is enough (for me) if you write (to me) once a month", is
Me basta con que me escribas una vez al mes.
The verb form escribas is in the subjunctive mood, present tense, second person singular. The non-emphatic pronoun me must be proclitic (i. e. it must come before the verb) here, as in most cases. You use the enclitic pronouns (i. e. after the verb, and written as one word) in the imperative mood, for example:
Escríbeme una vez al mes.
The subjunctive, as you see, very often appears within a subordinate phrase headed by the word que (such as Me basta con que…, Te pido que…, Me gustaría mucho que…). The imperative cannot go inside a subordinate like this.
Note well that que does not mean that the following verb must be in the subjunctive. That's not even a good rule of thumb for most cases.
Escríbeme is in the imperative mood, not the subjunctive. Escríbame is its formal equivalent (it's what you'd say to someone you're referring to as usted). Since usted, though second person, takes third-person verb forms, the formal imperative is formed using the subjunctive:
Escríbame pronto. = "Write(formal) to me soon."
Le pido que me escriba pronto. = "I ask you(formal) to write to me soon."
Finally, in Me basta con que me escribas…, you can drop con and the meaning will be the same. You can also drop either one of the pronouns me and the meaning will be mostly the same as well.