Hi and Welcome to Cute...do you mean by "bed sheet"...a whole cloth type quilt..one large piece of fabric that is then embroidered/quilted into a quilt?
I am assuming you will embroider it for your parents. Do you have the capability to combine designs on your machine or software? I really do not understand what you mean with "single bed sheet design"
I don't quite understand what you want.
A design like the first picture, but with a bear and flower - could you add a sketch or drawing ;
in bluework as your example or coloured; a border design plus a a curved one for the medallion or oval as in picture 2;
what size would you want that to be?
A lot of questions maybe, but your answer might clarify what you are looking for.
OK, so you want 1 design. That still leaves a few questions:
1. One colour only or more colours.
2. Bear + flower in one design - realistic bear + small flower? Can you make a rough drawing to show what you would like.
3. What size?
Welcome to Cute!
The blue floral design is free on http://www.embroiderydesigns.com/...
I am not sure it can be posted here, but I do know it cannot be copied. It is already available in the format you requested.