It is standard practice in good restuarants to wait until the customer asks for the bill, until it is brought over. As the customer it is up to you how long you sit there and if that is for hours on end, the staff just have to wait. If there is a time limit on tables, that should be made clear.
So it wasn't usual good restaurant practice to bring the bill with an item ordered ...unless of course the customer asked for it with that item, which a number of people may prefer ...all fine, because it's their choice.
So the restuarant were being rather rude and insure it was to shoo you away, but it was your choice to be leave sooner. You didn't need to leave quickly.
Personally, I would have said 'oh I didn't ask for the bill' and looked surprised. If at that point they had said 'but you didn't want anything more' or similar, I think I'd have replied with 'not right now, but perhaps in a while' or something similar. It's the kind of thing where I would raise my eyebrows at, but probably wouldn't be saying anything about. If I felt they were being pushy or it was a very nice restaurant where you just don't expect this kind of thing, I might mention it to whoever was on the door on the way out.....because decent restaurants won't want their staff doing this.
The thing is, I wouldn't feel embarrassed, just mildly miffed. The OP and her mother felt embarrassed and obliged to whizz off.
Mothers Day eh.....restaurants trying to pack people in and squeeze in as many covers as possible....all a bit greedy and short term, rather than considering if you'll ever be likely to return again.