Picking linden flowers is done when the flowers are open and still white, they are picked up with the bract (small leaf at the base of the flower stalk). This is also the time when they are most visited by bees and other foragers, such as bumblebees. Besides, the lime tree buzzes, it is well known. The risk of bites is almost nil, the insects being more absorbed by the flowers than by the picking fingers. You still have to avoid crushing a bee between your thumb and forefinger...
If the song of the lime tree brings out some fear, collect your flowers early in the morning while the bees are still sleeping. You will then spread them (the flowers, not the bees!) in the shade for several days to dry them, before putting them in tin boxes. (That's why I eat a lot of biscuits...to have linden boxes)
Other details on the problem of certain lime trees on the mortality of bees. Read before planting this tree so as not to choose the wrong variety.
http://www.bruxellesnature.be/tilleulargdangers.html