Some girls do avoid going on dates when asked due to being shy.
A good way to tell that this is the case is to observe how she behaves after the fact.
If you are noticing that she is still looking your way often, even though she may be trying to be sly by avoiding simultaneous eye contact, she more than likely wanted to go on that date with you.
If you also notice that she continues trying to be around where you are in a physical sense by constantly being within eye shot of you or tending to go where you go, albeit within the safety net of having her friends around her, there is a good chance that she wanted to go on the date with you.
Listen, there are a number of ways by which this can all be misleading and you may be getting the wrong cues.
In other words, are you entirely certain that this is a shy girl?
Even though she may not speak that often, she may simply be relatively introverted.
It doesn’t necessarily mean that she is shy.
You do have to be fully aware of this.
A good way to read on this is by how many friends she tends to have around.
If you constantly notice that she is with a variety of friends every time you see her, she may actually not be that shy.
In which case, her denial of the date may have been done because she simply didn’t like you as opposed to having done it because she was shy.
You should be very aware of this before deciding that she is the shy type.
Some girls can be very quiet around you but extremely extemporaneous when they are around people that they are comfortable with or acquainted with.
If you still believe that she is shy, you should watch for the cues that I mentioned earlier.
Is she still looking in your direction whenever you are not looking?
Is she still trying to be around you physically although she may hide herself inside the company of a few friends?
Is she often talking about you with her friends or colleagues?
If she is talking about you often with her friends or acquaintances, she would be doing so because she more than likely still likes you.
Oftentimes, the only way to find out that she is doing this is through becoming acquainted with some of her friends or colleagues.
At some point, they will begin to mention conversations that they are having and you may be able to eventually get one or more of them to tell you about who and what this girl often talks about.
If you are in that mix, she does like you.
Also watch for how often you see her at social events that you are going to.
She may often show up to these events acting as though she is merely there to be social but you will notice that throughout the event she tries to look your way.
She may not come up to you and talk to you but she is observing you.
These are all cues that she may have avoided the date due to her shyness but she still likes you.
You would have to ask yourself whether this is the kind of person that you are able to be patient with.