How long should it take for an experienced clarinet player to learn tenor sax?

My daughter plays clarinet in concert band and marching band. Her band director doesn't want clarinets in his senior jazz band, so she got "sent back to the minors" to play in the junior jazz band. We have a tenor sax and are looking to get it overhauled to get it into playing shape. She already takes private lessons on the clarinet and I cannot afford lessons on two instruments for long. I do think she should start out with an instructor so she doesn't pick up any bad habits while trying to teach herself. Would a couple of months of lessons be enough so that she can get started right and then continue on her own?