Actually there is a mistake in this sentence, which might be overlooked by native speakers but confuses non-natives. Correctly it would be:
Ja endlich können sich nun auch die ärmsten Tampons leisten und endlich das ständige Bindenwaschen sparen.
Bindenwaschen as a nominalistation has to be written together and with an upper case letter.
When you take a look at das Binden waschen sparen the article das refers to waschen:
She wants to spair the washing of the saintary pads.
And as you might know, every word addressed with an article has to be written in capital.
But now comes the connection betwen waschen und Binden. If you translate the sentence above into german again it woudl be:
Sie möchte das Waschen der Binden sparen
Now you can "merge" the two nouns Waschen der Binden into Bindenwaschen
So in conclusion the writer was just sloppy and filled in an additional Spacebar which makes the nominalisation appear as a noun and a verb without connection