Is it safe to be taking buspirone and Cymbalta together?

Yes

Hi, Please! Yes, these two medications can very rarely cause an interaction known as serotonin syndrome. Doctors are aware of this and will monitor you closely for any symptoms.
https://www.drugs.com/interactions-check.php?drug_list=441-0,949-2273&professional=1
Buspirone is an excellent medication for the treatment of anxiety disorders. I've been taking it with my other meds for over five years now. The only other option would be the highly regulated use of a benzodiazepine but most reputable doctors are no longer prescribing them because of the risk of addiction and long term side effects.
Stay in close touch with your doctor, but I think following her/his professional advice is wise to get you through this rough period.
I'm sorry for the loss of your mother. It will take time but there will come a time when you will have pleasant memories.

No it may not be safe. My experience with cymbalta is to check any med and sometimes food. There is a major interaction with these two drugs; with that said I would ask my doctor why he would suggest you take buspirone, at all. Do your research on reputable site, such as this one.