All those options - case management, MDS for example do usually require certification and experience in that field, in my area. I have never seen any CM job (hospital or SNF) that asks for less than 2 years CM or MDS experience and certification. Now, you will see that some in CM or MDS have learned and were sent for training on the job, but mostly that was years ago. Years ago they'd train anyone who was willing when CM was new - and I've met one or two people who were not even nurses, doing it in hospitals because they started so long ago! Overall the idea of employers sending you off for training is less common. I'm not a CM but have been really looking into just about everything these past years to find what is reality.
CM is hotly fought over of course by many nurses for the very reason you want to leave bedside. So does everybody else.
HH or hospice can be good or complete scams. I'd say many more are scams than not these days. Tough one, they can be worse to do than bedside in that you might be forced to work most the day and night to keep up on your charting work - can be most of 7 days a week to get it all done dependent on the employer. After all many of these just want you to admit and chart for reimbursement - patients don't receive much care anymore. I worked Hospice for a short time and felt that I worked for criminals, so I quit.
One thing, I'd not spend one dollar more on nursing if you can help it. Nursing can be a huge money pit with little return. I know it didn't use to be that way, but today it's totally a money pit.