Good thought Kakaliji!!
From Ashu's statements: "yahan bhi tum baazi maar le gayi Nidhi" & "Tumhare paas to sab hai, mere paas Baba ke siva kaun hai" we might get inspired to believe that Ashu might have been thinking of Nidhi's blood-relation with BB and might be having jealousy at their bond. But, in my POV, it was not Ashu's jealousy to Nidhi as BB's granddaughter and direct bloodline heir. He has never seen the love and comfort from any other elderly/parental figure than BB. BB though has never adopted him legally, but, raised him like his own child. Since, Ashu's haunted past as an orphan child still dominates him, he is again feeling insecure just at the thought of loosing BB.
That child in him has resurrected this time again and hence this childish dialogue of "Baazi maar le gayi". To me it seemed like just as any disappointed child upon loosing an opportunity envies other child's luck who is given the opportunity; the disappointed child in Ashu envied Nidhi's luck that she would get to spend all her time with BB whereas he wouldn't.
The other dialogue "Baba ke siva mera kaun hai" also came from him rather unknowingly that it would deeply hurt Nidhi. Prior to Nidhi's arrival in his life, his entire world had been limited to BB only. It's true that Nidhi is now so much an integral part of him and his life and Ashu too accepts this fact but still the importance that BB holds in life is not replaceable by Nidhi or anyone else. Ashu is a complex and layered personality and his inner demons pop up every time he is in a condition to loose something/someone he holds onto. He again starts feeling lonely, insecure and helpless and that's why feels that when BB would not be with him, he will be all alone. But, he surely doesnt think about the difference between his & BB's relation and the blood-relation between BB and Nidhi. -- my POV only.