My opinion is...you need to use Thioglycolate Agar to culture the microbes and observe their reaction. Thioglycolate is a semi solid medium that is enriched with a redox dye (resazurin) which turns pink when oxidized and remains colorless when reduced so it can be used to differentiate between oxic and anoxic regions of the medium. So introduce a small amount of your culture into the medium (sterilized) and observe their region of growth. If they grow in the oxic/pink region which is mostly the upper part of the medium where oxygen can penetrate, then you can comfortably conclude that they are aerobic
In addition to above even Sterile Moellers decarboxylase broth with and wihtout lysine both tubes overlayed with sterile paraffin oil can give additional information and also try Sterile Hugh Leifsons media one tube overlayed and one tube not overlayed with sterile paraffin oil--- to check oxidative and fermentative mode.
Anjali kindly read the attached file for more information on Thioglycolate broth and the principle behind its usage in differentiating microbes based on their oxygen requirements or tolerance.
In my opinion is sufficient if you grow the microbes (bacteria) in nutrient broth with agitation or with air, however, it is suitable totest bacterial growth under anaerobic conditions, without oxygen and air.
In Lysine decarboxylase to test whether organism is positive for lysine decarboxylase enzyme and formation of cadaverine and in Hugh Leifson to check whether the organism has oxidative or fermentative mode of metabolism.
I agree with Mrs. Atrayee Dey that aerobic bacteria can be cultured by using Nutrient Agar medium and in Nutrient broth. culture can be achieved by placing it in shaker.