Conjoint analysis: bias due to no-choice option and linear attribute

#1
At the moment I am analysing survey data using Bayesian estimation in R (bayesm package)

For my analysis, I have included a no-choice option (NoneOpt) that is coded as a series of zeros. However, I also have a price attribute (Delivery.costs). What I actually want to do is keep the price attribute as a linear variable. However, for the no-choice alternative (NoneOpt = 1) the zero is then considered as a linear variable as well. This leads to bias in the estimations according to the existing literature

In short, the main issue here is that the zero values of the no-choice options act like 'real' values for the linear price leading to bias in my estimates.

Example data:

Example.PNG

Anyone familiar with this issue and/or workarounds?