I perform about 30 stress echoes per week in my job. The vast majority of these tests are performed to differentiate patients with significant coronary artery disease from those that don't (saving them an angiogram). They are usually reserved for patients with suspicious symptoms (crushing chest pain on exertion) or extreme risk factors (strong family history, smoking, high cholesterol, type 2 diabetes etc). You generally only need to achieve 85% of your predicted maximum heart rate (based on the 220 minus your age) and show no suspicious signs (chest pain, ecg changes, wall motion abnormalities) to pass tbe test and be classified as low risk for a heart attack in the next two years (with greater than 99% accuracy, so even though some of you will question the 220 minus your age thing, it does work for this application).
So, you will notice that none of this applies to your situation. What you more likely need is to wear a holter monitor (an ecg recorder) while riding your bike and have a look for any rhythm change as opposed to just the rate going up normally. Chances are you just have a higher than average max heart rate for your age, but you're right to take the safe approach as you may be flipping into an abnormal rhythm. If this were the case you may have symptoms like palpitaions, dizziness or unreasonable breathlessness, but best to check.