Yup.
The amount of heat in the water depends upon its volume but the rate at which heat is lost depends upon its surface area. If, say, you increase the volume by 8 (equals 2 cubed), you only increase the surface area by 4 (equals 2 squared). So you've got 8 times as much heat but only 4 times the area for it to dissipate through, so it's retained for longer.
That's why the contents of a small Thermos flask, holding just a single cup of coffee for one person, cool down very quickly but the contents of a big Thermos flask, holding enough coffee for an entire football team at half-time, remain hot for far longer.
The same will apply to your hot water bottle.