I know this is an old question, but it's still worth tossing in my two cents.
I'm not really sure you really want a date axis for your bar chart, or even a bar chart, given the vastly irregular spacing of your dates and the way Excel spaces bars along a date axis.
Below I show your bar chart on the left. The vertical axis has a so-called Text Scale, meaning each date has a single slot along the axis, and the dates are treated as non-numeric categories.
To the right, I've changed the axis to a Date Scale, where each day has its own slot, one day wide, along the axis, and the bars are positioned according to the numeric values of the dates.Since each bar must fit within its slot, each bar is less than the width of a day, so they are more like hairlines than bars. If you had two bars for the same day, they would plot one in front of the other.
Below the bar charts is a line chart. The date scale is horizontal, which is more natural for humans to understand. The thin bars are replaced by markers, which are easier to see. Multiple points on the same day are represented by multiple markers, so they don't obscure each other as in the bar chart.