Answer:

Because you have Ubuntu installed using Wubi, unfortunately, you won't be able to choose which OS you want to boot if Windows is hibernated.

Explanation:

From the comments, it seems that you have Ubuntu installed using Wubi, which means that you installed Ubuntu inside Windows. This is because in the comments, you said "Ubuntu is installed on partition H:", which probably means that you can access this H: partition from your Windows OS and see a folder called "Ubuntu" inside it, correct? If yes, read on:

When you restart your computer, it boots BOOTMGR by default, which is the Windows bootloader, and gives you the OS choice (Windows or Ubuntu). If you select Ubuntu, you go into GRUB. All good so far. However, the first thing BOOTMGR does (before giving you the OS choice) is it first checks if there is a hibernated OS. When it finds that Windows is hibernated, it directly boots into it, without giving you the options. This is what is happening on your machine. GRUB, on the other hand, does not do this.

How would you overcome this? By making GRUB the default bootloader (with Ubuntu and Windows as OS choices), not BOOTMGR. This, however, is in the case if Ubuntu is installed on a separate partition (a partition formatted in another format, ext4, that is not accessible through Windows). But because your Ubuntu is installed through Wubi, meaning that it's on the H: partition, meaning that it's on a Windows partition, this partition is part of the hibernated Windows! Get it =)? So we can't install GRUB as the default bootloader and ask it to boot Ubuntu from the hibernated partition, because then it will _{(I think)} attempt to destroy the "hibernated data" and basically shutdown your Windows (and you lose all your unsaved data when you hibernated), then attempt to boot into Ubuntu. Get it now?

So in the end, unfortunately, I don't think it's feasible. Your solution would be to uninstall Ubuntu/Wubi, and install Ubuntu from scratch on a separate partition. This solution will uninstall Ubuntu/Wubi and will delete everything in your Ubuntu, so make sure you backup the files you need.

Another possible solution is to convert (migrate) your Wubi Ubuntu into a full, normal Ubuntu installation (put in on a separate partition). This way, it will copy over all your content, and you should find all your files the way they were (**although it is always advisable to backup your files whenever playing around with OSs). The steps to do this solution are detailed here: How to convert Wubi install into regular install? Here is a brief description of what you'll be doing:

1. Boot into your Wubi Ubuntu.


2. Using gparted, create an empty partition big enough to house your Wubi Ubuntu (just make a partition as big as your H: partition, or as big as the "Ubuntu" folder). Choose ext4 as the filesystem type for the new partition.


3. Download the script from that question, and run sudo bash wubi-move.sh /dev/sdaX, where sdaX is your new partition you created in step 1 ("X" is a number, e.g. sda6. You can see the number of that new partition in gparted next to the partition).

Again, this is a brief description. Visit the question I linked and read the whole thing.

Having said all of this, my advised solution would be to:

1. Backup everything you want from your Ubuntu.


2. Completely remove Ubuntu Wubi (How do I uninstall Wubi)


3. Install Ubuntu from scratch.

If your H partition was only meant for Ubuntu, then you can use that whole partition to install the new Ubuntu.