I've been to Disneyland from Shinjuku by both ways (ie JR and shuttle bus).
For JR, I remember we needed to walk for quite a long distance in the Tokyo Station for getting change to the proper line.
For bus, there are free shuttle bus for some linked hotels with Disneyland. Though the schedules are fixed, I think it's quite convenient esp if you are going with small kids. Last time (Jan 09), we stayed in Keio Plaza at Shinjuku and had taken this free service back from Disneyland to Keio Plaza. Please also note that advance reservation of seats may be required (last time, I've just sent email to the Hotel and they responded in a very short period of time.)