Any advice regarding guilt about putting my mom in hospice?

Thank you all for your thoughtful responses. I feel both sad and guilty.
Mom died on December 13 2017. She lived with heart failure for 6 years. On Thanksgiving Day 2017 mom fell and was brought by ambulance to her local hospital. I asked the hospitalist if mom qualified for palliative care, but a cardiologist on call said that hospice, in her case, would be more appropriate. We started home hospice November 30th (her 87th birthday) however, she suffered a bowel impaction on December 8th and entered inpatient hospice that evening. Mom was very lucid during her stay. Her wonderful caregivers finally resolved the bowel impaction on day 3 and announced that she was ready to return home. The problem was that she was now totally unable to stand at all. The staff told us that mom could remain inpatient while we tried to arrange for her return home as a totally immobile person. Mom begged to go home, and I had to tell her to be patient - that we needed time to make arrangements for more help. Well, the next day hospice called to tell my family to come and say our goodbyes. I was the last one to arrive and mom said "I don't want to go" to which I replied "it's okay, mom, don't be afraid. It's okay to let go". The nurse started the morphine drip, and mom turned on her side - in a fetal position. Our family surrounded her and basically watched her die - which took about 24 hours. I know she was somewhat aware for the first several hours because she pointed to her lips, which were parched, and I swabbed them with a wet sponge the nurse left with us.
Thank you all for reading this post. I knew the upcoming holidays would be difficult, but I was not prepared to feel so sad and guilty.

You can't "put" Mom in hospice. You can request it, but she is evaluated to see if she is within their criteria. She must have been if they excepted her. Yes, no extreme measures will be taken to keep her alive. She will be kept comfortable and free from pain. The NH wanted to send my Mom to the hospital because she was losing the ability to swallow. This is a sign the body is shutting down. I said no and requested hospice. I knew she wouldn't want to be touched and poked and prodded. Her Dementia journey had been at least 6 years long. She needed to not be bothered. She passed peacefully a week later. She was 89.

My daughter is a nurse and says "the elderly are living past their expiration date".

Is it guilt or is it sorrow? When I got a call in the middle of the night asking me whether they should send my 99 year old mother to the hospital I hesitated for a few seconds before I said of course not. Even when the answer is obvious it is a hard choice to make and there are no perfect answers, unfortunately.

Why would you feel guilty? Hospice provides round the clock care for people at the end of life. Do you feel that you need to do heroic measure to keep her alive? Is she cognizant of what’s happening? How does she feel? Does she have an end of life plan/wish?

If you provode more detail, maybe we can give you better advice.