There is no such thing as a good bidah. As the prophet (swt) said " "For every newly-invented matter is an innovation and every innovation is misguidance...", and our measuring stick for what is permissible and what's not is from the Sunnah and then from the companions. So ask yourself was this practiced during the time of the Sahaba and you should have you answer as they were the best of men.
And Allah says in Surah Maaida "
This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion. But whoever is forced by severe hunger with no inclination to sin - then indeed, Allah is Forgiving and Merciful."
Even something as small as the tusbax is a bidah as the Prophet used to use his hands to read his adkhar. Read below:
The Sahaba’s Opinion Concerning Bid’ah
Amr ibn Yahya narrated his father told him, "We used to sit at Abdullah Ibn Masood’s house before Fajr prayer. If he exited we would follow him to the musjid. Abu Musa Al-Ash’ari then came to us and asked us, ‘Did Abu Abur-Rahman (Abdullah Ibn Masood) come out yet?’ We said, ‘No’, so he sat with us till he emerged. We all stood up when he exited. He (Abu Musa Al-Ash’ari) said, ‘O Abu Adur-Rahman, I just saw something which I did not recognize, and I did not see, all thanks to Allah, but good.’ He (Ibn Masood) said, ‘What is it?’ He (Abu Musa) said, ‘If you live you will see it. I saw in the musjid people sitting in circles waiting for the prayer. In each circle there is a leader, and they have stones in their hands. He (the leader) would say, ‘Say Takbir (Allahu Akbar) 100 times’, so they say Takbir 100 times. He (the leader) would then say, ‘Say Tahil (La Ilaha Illa Allah) 100 times’, so they say Tahil 100 times. He (the leader) would then say, ‘Say Tasbih (Subhana Allah) 100 times’, so they say Tasbih 100 times. Ibn Masood said, ‘Did you not order them to count their evil deeds, and guarantee them that none of their good deeds will be lost?’ Then he and us left till we reached one of the circles. Then he (Ibn Masood) stood next to the circle and said, ‘What are you doing?’ They said, ‘O Abu Abdur-Rahamn, (these are) stones that we count our Takbir, Tahil, tasbih, and Tah’mid (Alhumdu’lillah).’ Ibn Masood said, ‘Count your evil deeds, for I guarantee that none of your good deeds will be lost. What is the matter with you, O nation of Muhammad? How soon you come to your destruction! The companions (of Muhammad) are still many, these are his clothes still not worn out and his cookware did not break yet. By whom my soul is in His Hands,
you are either following a religion better than Muhammad’s or followers of a way of evil.’ They said, ‘By Allah, O Abu Abdur-Rahman, we sought only what is good.’ Ibn Masood said, ‘Many people seek good, but they do not reach it. The Messenger told us some people who read the Qur’an will not have the Qur’an leave their throats (to their hearts). By Allah I do not know if most of you are from them.’ Then he left them. Amr Ibn Salamah said,
‘We saw most of those people fighting against us, in the battle of Nahrawan with the Khawarij.’" (Tirmidhi)
So imagine celebrating the Prophet's birthday? Which is even worse since you're imitating the kufar as the Christians do the same thing with Christmas.
If you guys have free time look into this website:
http://www.bidah.com/. Very beneficial.