Here's some great advice from Jessica Willingham writing for Bustle.com.
"It's a great idea to wash a new brush... especially if the bristles were exposed. Countless hands, faces, and who knows what else has touched them before you, so you should definitely give it a wash!...Let me explain why.
"Cleanliness is a huge benefit from washing your brand new brush. Still, there are other reasons to suds up. Washing the brush first thing when you get home will remove any loose bristles and anything that may have come in contact with them during the manufacturing process. Seriously, who knows how long they were sitting in a warehouse. Washing will also remove that stale smell. What's more, you may also see some color bleed in the initial wash, removing any extra dye that you definitely don't want mingling with your foundation.
"Washing will also help soften and condition your brushes, prepping them for use and extending their lifetime...."
Read the full article here