I can’t answer to the process time on the slipcasting, but kiln turn around is highly variable depending on the volume and types of work on the shelves. Which is very high right now due to lots of classes (yay!), the start of the Christmas push (yes, already), how long it is taking pieces to get dry (slower when cool and humid), and the size/shape of the piece (large and/or awkward pieces will take longer to fit into firings). If the planets come into alignment, a one week flip for finished green to bisque is possible, but a more safe estimate is two (to three, if large/weird) weeks at this time.
All that said, there are options:
We have some leftover bisque from Open House that you are welcome to glaze. There is a suggested price on the bottom (all very, very cheap, sub $5 options) and you can drop a payment into the black box next to the glaze. If you go this route, I recommend checking them out soon, selecting, paying and taking home until class. Good option for learning skills before tackling your personal piece.
Put a (big, noticeable, friendly!) note on your greenware with the date of your upcoming class and, /if possible/, kiln loaders will attempt to help you out.
Also, check with your instructor! It’s possible they are intending to do a special firing of class pieces. This may already be arranged.
Also, welcome to DMS Ceramics! We have a monthly Clay ‘n Coffee pottery/social shindig that is a fun and casual way to connect with our ceramics community, we’ll be talking mugs at the November meetup.