How to determine the dimensions of a bixin molecule?
There is a paper on bolaamphiphiles (1) where it is stated that measured surface area corresponding to the area of a bixin molecule lying on the water surface with most methyl groups pointing outside is approx. $\pu{1.0 nm^2/molecule}$ at zero pressure. If the methyl groups were parallel to the water surface, a molecular area of approx. $\pu{1.7 nm^2/molecule}$ would be occupied.

Also, there is a linear size of a single molecule stated as the following:


  Bixin therefore constitutes a valuable starting material for various bolaamphiphiles which can be tied within lipid membranes. Its molecular length is about $\pu{3.1 nm}$ in the all-trans configuration. 


I think it might be worth for OP to have a look at the full-text (1) paper as it also discusses various methods of characterization and altering of bolaamphiphiles. 

A few years later a crystal structure has been published (2). There is not much to add, as it seems like there is no contradiction with the data obtained with reflection spectroscopy (1). Here are the notable linear dimensions of cis-bixin and overall geometry in 2 projections:





(1) Fuhrhop, J. H.; Krull, M.; Schulz, A.; Moebius, D. Langmuir 1990, 6 (2), 497–505. DOI: 10.1021/la00092a034
(2) Kelly, D. R.; Edwards, A. A.; Parkinson, J. A.; Olovsson, G.; Trotter, J.; Jones, S.; Malik, K. M. A.; Hursthouse, M. B.; Hibbs D. E. 1996, J. Chem. Res., 446, 2640