The scales of Ananda Bhairavi are as follows :
Aarohanam (Ascending) : S G2 R2 G2 M1 P D2 P S’
Avarohanam (Descending) : S’ N2 D2 P M1 G2 R2 S
Though it uses all the seven notes, the Aarohanam contains vakra proyagam (zig zag notes in the scale) so it is not a Melakarta raga. It is janya raga, derived from Natabhairavi, 20th on the Melakarta scale. It uses anya swarams (external notes) as compared to its parent raga, using G3, D2 and N3 in certain phrases.
Ananda Bhairavi and Reetigowla share the same notes, but the prayogas are different. This is an excellent demonstration of the differences between the two ragas from ragasurabi.com:
The best known compositions in this raga are Marivere Gati and O Jagadamba by Shyama Shastri. Tyagaraja Yoga Vaibhavam and Kamalamba Samrakshatu by Muthuswami Dikshithar, and Paluke Bangara Mayena by Bhadrachala Ramadas are also familiar to most rasikas.
Tamil readers may enjoy the following discussion of the raga by Charulatha Mani.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.