Shaikh Ibnul U’thaimeen was asked if using a ‘Tasbeeh Bead’ is Bidah. He replied:

“Using a ‘Tasbeed-Bead’ is JAIZ, however the best thing is to count tasbeeh using finger tips, because the Nabi said “Count with your fingers as they will be made to speak.” Sometimes there maybe riyaa (ostentation) in holding a tasbeeh bead. And those that use the tasbeeh beads most of the times you will find that their hearts are not present. So they say tasbeeh with their beads but they are looking left and right. So the Fingers are more virtuous and better.

[Majmooah Fatawa wa Rasaail Ibnul Uthaimeen 13/242]

In another fatwa Shaikh Ibnul Uthaimeen expounds on the points of fingers, riyaa and concentration. However in that detailed fatwa he still stressed the following:

“The ‘Tasbeeh-Bead’ is NOT a  Bidah Deeniyah (religious innovation). This is because a human does NOT intend to worship Allah by it. Rather he simply intends to count the Tasbeeh or Tahleel or Tahmeed or Takbeer that he is saying. So this is a means and not an objective. However the best is that a person uses his fingers.”

After expounding on the points of fingers, riyaa and concentration he states:

“After all of this, making Tasbeeh with the Tasbeeh-Beads is not a Bidah in the Deen. The Bidah that is prohibited is the Bidah in the Deen. Saying Tasbeeh using the beads is only a means to count the numbers. It is a less preferred and less virtuous means. The best is to use fingers in counting the Tasbeeh.”

[Majmooah Fatawa wa Rassail by Ibnul Uthaimeen 13/240-242]

والله الهادي و به التوفيق

Also see here.