The expression "be receptive to (something)" ends in the preposition to and must be followed by a noun phrase. The to that appears here is different from the word to that appears in the infinitive of a verb (as in "to know").
"Being approached by me" is a noun phrase. The word "being" is a verbal noun. This -ing form refers abstractly to the action denoted by the verb.
For example, one can say "Living in Oklahoma is a lot of fun." Here "living in Oklahoma" is a noun phrase that refers to the state of being a resident of Oklahoma. The example of "being approached" is slightly more complicated because "to be approached" is in the passive voice, but the principle is the same.
Neither of the two suggestions you made is possible. In "receptive to," the word to can only be followed by the -ing form of a verb.