I didn't actually do much research; I just went through several pages of hits for aspirin alcohol and low-dose aspirin moderate alcohol. I saw consistent enough information to convince me:

• never to take them at the same time, sample:

  In a paper published in the Journal of the American Medical Association, researchers at the Veterans Administration Medical Center in the Bronx found that taking aspirin one hour before drinking significantly increases the concentration of alcohol in the blood.

• that the nasty interactions only seemed to happen at 21+ drinks per week, sample:

  There is no proof that mild to moderate alcohol use significantly increases the risk of upper gastrointestinal bleeding in patients taking aspirin, especially if the aspirin is taken only as needed. However, people who consumed at least 3-5 drinks daily and who regularly took more than 325 mg of aspirin did have a high risk of bleeding.

That, in conjunction with the 2010 Dietary Guidelines for Americans, was enough to convince me to combine 81mg of aspirin in the morning with 0-3 US standard drinks in the evening at an average of 1.0/day. I'd like more information, but I haven't had time to dig it up yet and combining them seemed like a lower-risk provisional decision than inaction.

I recommend you do your own research and talk to your doctor, but maybe someone will find that information to be a helpful starting point.