Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
As to what follows:
In response to your question, we say, and with Allah Almighty lies all success:
There is no contradiction between the verse and the hadith, for what is negated here is enumeration, i.e. encompassment. This is true, for no matter how much a slave is given of short expressions that contain vast meanings, powerful explanation and eloquence of the tongue, he still will not encompass Allah Almighty with praise, nor will he ever be able to. Imam Malik (may Allah have mercy on him) said, “It means that, ‘I cannot enumerate Your blessings, kindness and praise, even if I worked really diligently to praise You.’”
Moreover, this negation does not mean being incapable of praising with praise in general or praise in its essence; rather the incapability is in encompassing it all in detail. As for overall praise, it is something capable of achieving, among which are all words of praise that have been narrated from the Prophet (peace be upon him).
As for the reason we cannot enumerate His praise, it is because enumerating His praise is part of encompassing His essence, His names and His attributes; and this is impossible for creation. He Almighty said:
“But they will never encompass anything of His knowledge.” [Taha 20:110]
So no matter how much we praise Him, we will never reach the limit of perfection, enumeration and encompassment, because we do not know all of His names and attributes, nor all of the reasons for praising Him.
Another reason can be mentioned, and that is that the blessings of Allah Almighty upon His slaves are many; there is no limitation of them in terms of their categories and kinds. Every blessing requires praise, which is something His slaves are incapable of, not encompassing or enumerating them. Allah Almighty said:
“And if you were to count the blessings of Allah, never will you be able to enumerate them.” [Ibrahim 14:34]
So all praise is due to Allah as we say it, all praise is due to Allah more than what we may say and all praise is due to Allah as He says it. The heavens and the earth and all that is in between are abound with His praise, and all else that He wills are abound with His praise also.
He spoke the truth who said:
If we praised You with a single praise
How far it would be to enumerate sand or drops [of water]
However, we bring forth what we are capable of
And he who exerts the effort has the right to be excused
As for bid`ah, it is every newly invented path in the religion, striving to rival with the Shari`ah; the objective of treading upon it is the same as the objective of treading upon the path of the Shari`ah. Thus, a bid`ah is every act of worship or belief that was innovated after the Messenger (peace be upon him), while its means were available in his time and there was nothing to prevent him from them; yet he did not know of them, nor believe in them, nor command them, nor acknowledge them.
Moreover, bid`ahs that the Messenger (peace be upon him) described occur in statements, acts of worship, beliefs and actions. Ibn Taymiyyah (may Allah have mercy on him) said, “Bid`ahs are of two kinds: one that is in statements and beliefs, and another that is in actions and acts of worship; the latter of which includes the former, and the former of which invites to the latter.” [Majmu` al-Fatawa, vol. 22, p. 306]
What is obligatory is to beware of both kinds, for bid`ahs in all their various forms and kinds are evil for the one who performs them, and include defamation of the Shari`ah, claiming it to be deficient, and also defamation of the Messenger (peace be upon him); as a bid`ah is something supposedly good meant to get closer to Allah through, yet he did not guide us to it. As such, this is considered a shortcoming on his part in conveying.
Expounding on these meanings is too constrained for this short answer.