Using cell data as partial text search with COUNTIF

Usually, when you want to count the amount of cells containing a text you can use wildcards.
Like =COUNTIF(A:A,"*NAB*").

I want to count a lot of different things, so I have all what needs to be searched for in a column.
Usually, you use =COUNTIF(A:A,B1).

However, I need a combination of both. Something like =COUNTIF(A:A,"*"B1"*").
Is there any function which allows for such constructions? Or how should a workaround be made?

It's very important to note I'm looking for text in cells that contain more text than only the text I'm looking for (therefore the wildcards).
Preferably, the source text is in one column, the text which needs to be looked for in a second column and the output of the function in a third column (seperate output per lookup text).

Originally Posted by daddylonglegs

=COUNTIF(A:A,"*"&B1&"*")

Works like a charm, thanks!