Better to just bike a little on vacation maybe? You could just take the train up and rent a bike in SF and "bike the bay." They also rent bikes around Santa Monica pier.
If you must do the tour... your best chance to make this work is to find a 90's MTB on (Craigslist?) and seal the deal before arriving. Bring a large seat and handlebar bag with you, or buy a mid level rack and saddlebags. I would also go with thinner tires, which can be had at performance bike for less than $30/pair.
I found this one on SFB Craigslist that looks to be in great shape: "PRICE REDUCED! Original-Vintage Fisher Hoo Koo E Koo - $199 (san rafael)"
PRICE REDUCED! Original-Vintage Fisher Hoo Koo E Koo The seller may think you are a scammer, so make sure you indicate that you will give the guy cash in hand when arriving, and offer to send him a deposit.
After the tour, there are several used bike shops in LA. Coordinate with them BEFORE arriving to consign the bike and sell it for you. Then you can make a clean getaway.
In case you need it, there are trains that run up and down the coast. Take a look at the Amtrak schedules to know where they stop.