jeevikaa- You are mixing 2 things here. for living persons, animated nouns, pets, the a before the noun is called Personal A. Here A is a preposition needed all the time after the verb ir / to go, voy al (a el) restaurante, él va a la playa.
At least in Chile, this would normally be phrased "Yo voy a acostarme." They would not say "I am going to bed" per se but would use the verb acostarse. Obviously they might say something like this in Miami (heavily contaminated Spanish).