Can We Mediate Without Being in the Same Room?

Yes. Mediation is a highly adaptable process. Sometimes people are in the same room through the process; sometimes people are not in the same room at all. More often it is a combination of these two possibilities.
If there is a high level of conflict, or other reasons why you do not wish to be in the same room as your former spouse, the process can be what is called a “shuttle mediation”. In shuttle mediation, each of you is in a different room throughout the mediation, and the mediator “shuttles” back and forth between rooms (hence the name). Shuttle mediation can still be very productive and is just as likely to result in a settlement.
Shuttle mediation is more common where you attend mediation with your lawyer (rather than on your own). However, shuttle mediation can also be done without lawyers.
If you don’t wish to be in the same room during mediation, talk to your mediator about it during your intake meeting. She will design a process that will work for you and your former spouse, respecting your concerns.