I use the following rule: There is a link from A to B if A is "one of the causes of" B. And generally, there is a link from A to B OR from B to A if there is a some correlation (not necessarily linear) between the values of A and B. The true rule is more complex, regarding conditional independence (see for example the tutorial on BN by Andrew Moore at http://www.autonlab.org/tutorials/bayesnet.html)
Thus, a reasonable solution would be:
a) all variables point to the bicycle variable, since for all you can make the argument that for example raining or not will definitely have an impact on whether or not a person will bike to work.
b) there are some relationship between the meteorological variables, although exactly which it is not totally clear to me. For example, if this refers to people living in temperate zones, then there is a link from temperature to rain, not a causal relation, but knowing the temperature changes your belief whether it is raining, since it will not rain if the temperature is below freezing! It is not clear to me how wind is related to the other variables: is it more or less likely that it will be windy if it is raining or not? If it is, then there is a link from rain to wind.
c) If you want to be complete, there are some links between the socioeconomic variables: the number of cars probably depends on the age, since older people are more likely richer than young people (and also much older people may have less cars because they drive less?). Thus a link from age to cars. Also there may be a link from gender to obese: are man more likely to be obese than woman? (I dont know). Also a possible link from age to obese (possibly the distribution of obese-ness is not constant across age).
(sorry I do not have at the moment any software that would allow me to draw the net and post it as part of the answer).