If it had been a long time since he regenerated, and hadn't looked in the mirror yet, I don't know that it necessarily had to be a conscious decision, it could simply be that he got busy and forgot to bother (Although, it probably did start out as shame). The way The Doctor flits about from one adventure to the next, he pretty much allows himself to be carried along from one adventure to the next. Although he claims to keep track of his age (And therefore the passage of time), I don't think he really does notice the passage of time. If he was traveling alone, I could easily see how he wouldn't know the difference between 2 years or 100 years passing by since Regeneration before meeting Rose