what other solution is available if I want to keep my IAM Identity center in us-east-2 and also want to deploy Bedrock studio

Hello.

Unfortunately, Bedrock Studio and IAM Identity Center cannot be configured in different regions, so they must be configured in the same region.
https://docs.aws.amazon.com/bedrock/latest/userguide/administer-create-workspace.html

AWS Identity Center must be enabled in the same AWS Region as your Bedrock Studio workspace. Currently, AWS Identity Center can only be enabled in a single AWS Region.

In other words, there is currently no other way than to delete the IAM Identity Center settings and reconfigure them in us-west-2, or wait for Bedrock Studio to support us-east-2.
https://docs.aws.amazon.com/singlesignon/latest/userguide/regions.html#delete-config