First, I must say.. Wow! Dina... sounds like you have moved into a gardener's paradise... Lovely... know you will enjoy.
... And, thanks Wingdesigner and Jess for the suggestion of liriope. The leaves in Dina's pictures do look very much like a plant that I have that I have been meaning to take a picture to post here and ask about. It fits the description of liriope (guess that's why I posted about the different ways in which the lily or the grass shoots up)...
It's interesting that the liriope is pegged as 'lilyturf'.. does seem to look like both a lily and a grass, and I have found that it shoots up like an ornamental grass with the first blades coming up lying flat against each other.
If it is the same thing I have in my garden, and I suspect it may be, here's my experience of it. I first saw this plant in Florida in public spaces such as malls used as a ground cover. I liked the look of it. Not sure how I ended up with some in NY, but I did... I planted it as a border and loved it for the first year, but then .. hmm.. it took over and now I am having a mini battle... Well, I ended up removing it from the garden beds where I had used it as a border and have isolated it to areas where it can spread freely. To be fair to the plant, I was off my feet for a little while so the garden had gone neglected, free to be *smile* for that time. Perhaps, if I had kept on top of things, this plant would not have taken over, but this has been my experience, that it can spread wildly.
The plant I have does have the hyacinth like blooms and is drought resistant. In fact, it seems to grow happily just about anywhere and doesn't require any care.
Again, would be very curious to see what your plant turns out to be. I will pull up one of the ones I have to see if it has the bulbs you mentioned.