I remember been told to stay in bed when on antibiotics as a child but don't know the reason why.
Is it sound?
Is there any negative health effect?
Children, the younger they are, the more they are susceptible to febrile seizures which can occur during an infection. The safest place to be whilst having a seizure is on a soft surface like a mattress, not say, climbing a tree or swinging across a river on a rope. The above reference gives that it is best to place the patient in the recovery position to prevent choking on vomitus. This can be done if the child is in sight of the parent/guardian, which may best be done on the sofa or in bed, depending on the layout of the house.
As an adult, you may well be able to function relatively normally with a bacterial condition, but if you have a fever and you exercise, your temperature may reach dangerously high, ie. >= 38 Celsius, whereupon you may seize, which could be dangerous depending on where this happens.
Two facts are also relevant:
1/ Antibiotics can and do put a strain on the kidneys.
2/ A large amount of aerobic exercise - such as running a marathon - will cause the breakdown of a certain percentage of erythrocytes in the blood and a release of myoglobin in the damaged muscles (this is perfectly normal). This also stresses out the kidneys. Conditions such as Rhabdomyolysis make matters worse.
The Above two items occurring at the same time may cause irreparable kidney damage, leading to necessitate dialysis or transplant.
Tell your medical professional if you plan such strenuous activities, and take their advice is the best thing you can do here.