#Ask your DM
For the sake of completeness, the relevant part of the Wild Shape feature:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
— Player's Handbook, p. 67
The Bardic inspiration feature you want to retain and so be physically capable of:
You can inspire others through stirring words or music. To do so, you use a bonus action on your turn to choose one creature other than yourself within 60 feet of you who can hear you.
— Player's Handbook, p. 53
Stirring words are probably out, but whether a given beast form is able to perform stirring music is not something addressed by the rules. It is up the good sense of the players (in this case including the DM). Make your case for tapping your paws, or performing some sort of birdsong, to the DM (and the rest of your table). Personally, I would be inclined to allow it for a number of forms — for how funny it can be if nothing else — but have issues seeing how some, like a snake, would be capable.