Answer: Great question. The Medical Directive for Cardiac Ischemia does list current active bleeding as a contraindication for ASA. That being said, it is a judgment call as to the risk benefit ratio for ASA administration in the setting of acute MI and CHF (large) vs the relative risk of worsened bleeding if that bleeding is small (such as we see in blood tinged sputum for CHF patients as you describe).
The intent of this contraindication would be for patients who have active significant bleeding which is hard to define in a written all inclusive medical directive. Massive hemoptysis or hematemesis, bright red blood per rectum or melena, obvious external bleeding would be examples of what would be considered contraindications (not a complete list) in our mind, but a small amount of pink frothy sputum or blood tinged sputum would not.
Bottom line: if you as a paramedic are concerned that there is more than a minimal amount of bleeding, then document your concern and do not administer ASA.
If you feel there is a minimal or negligible amount of bleeding happening, given the benefit of ASA in STEMI, our direction would be to administer the ASA.