Several ideas and techniques from the CFAR workshop are relevant:

• Value of information: how much better can I make decisions after getting this advice?
• Cultivating curiosity: gee, I wonder what advice I'll get?
• Overcoming aversions / comfort zone expansion: what motives do I have for avoiding asking for advice? Does thinking about asking for advice make me feel bad? Do I view myself as someone who doesn't ask for advice? What do I expect will happen if I ask for advice and, taking the outside view, how realistic are those expectations?
• Evaluating advice: now that I've gotten some advice, how much should I trust it (taking the outside view again)? Is the sample I've chosen to ask for advice from biased? How independent is the advice that I get from multiple people? When I asked for advice, did I accidentally prime the person I was asking in a particular direction?

The workshop included a practical session on comfort zone expansion (we went to a mall and did mildly uncomfortable things involving strangers) which I found helpful, mostly because it helped me internalize social pressure in the direction of comfort zone expansion. At the workshop this was abbreviated as CoZE and there was a half-serious idea floating around of awarding "CoZE points" to people whenever they expanded their comfort zones, which is the main technique I used the last time I tried asking for advice. (The other technique I used was a social commitment mechanism, but explaining how that fit in would make the story too long.)

Any advice on how to ask for advice?

Try explicitly admitting to them that you care more about getting the job done correctly than appearing to be competent while doing the job.