All ryokan would accept foreigners, this should not be an issue at all.
I would recommend to use jalan.net to reserve a ryokan in Kusatsu, this might be the largest choice available. The problem is that everything has to be done in Japanese. You will find detailed instructions here :
http://www.secret-japan.com/forum/viewtopic.php?t=439
Alternatively, check our link section for more information on reservation of hotels/ryokan :
http://www.secret-japan.com/forum/links.php?t=sub_pages&cat=10
Be however aware that usually reservations are not carried our by email - phone or fax is more the rule; so try to reserve online if you can not call.
sanji
[MOD] This thread has been moved to the "Discussions" area. The "Guides" section is only for posting travel guides. Thanks.