You have several options.
A taxi ride will be direct, but will cost you somewhere in neighborhood of $40 to 50 dollars one way (+ tip).
Mears offers a shared shuttle service (by bus or van) which runs around $20 per person round trip. The trade off is you will likely make several stops around Disney before heading to Universal, and the times for pick up/drop off might not leave you the full day at Universal. Getting there early to beat the crowds for Harry Potter is important.
I don't know how many people you have in your party, but your best option might be renting a car for the one or two days through Alamo, which is on site at the Car Car Center near Magic Kingdom. They are open 6 a.m. to 8 p.m. Monday thru Friday, and 6 a.m. to 6 p.m. on the weekends. They also offer a free shuttle from your Disney resort to the center and back. Since you are going in October, you should be able to get a decent rate. Check out mousesavers.com for different discount codes - and keep checking right up until you leave, as you don't have to pay up front (or even put a credit card in) for rental car reservations. Just keep cancelling and rebooking at a better rate.
Hope this helps!