I’m not sure why you are including terms like "var_1*covar_1" in the model, which adds a particular type of interaction effect in Bambi. Is that what you want?
On the other hand, if you have a response Y and three predictors X_1, X_2, and X_3, no matter their nature, you would do
bmb.Model("y ~ x1 + x2 + x3", data)
without having to multiply the predictors by their coefficients (because these are the ones estimated with the model).
If you have many more predictors, you could do something like
predictors = ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10"]
formula = "y" + " + ".join(predictors)
bmb.Model(formula, data)