Investing into Bitcoin with a budget in mind wouldn’t be quite easy, Bitcoin is a very volatile assets so it wouldn’t be very easy to have an amount in mind to use in investing, that is why I think it’s more reasonable to accumulate gradually on a weekly or monthly basis depending on when you’ve have a discretionary funds, and planning on budgeting will definitely make us not to accumulate much bitcoin considering the volatile nature of bitcoin , because there are times when Bitcoin would increase and times when Bitcoin would decrease, having budget in mind would probably make us not to exceed our budget, Waiting to get whatever amount of budget set aside before starting to invest would be a waste of time because you might not get that budget which you planned.
At this point, instead of using budget why not we replace the word with "target" because budget might actually mean we wont exceed that amount no matter what which may not be possible. Investors sometimes get overwhelmed after accumulating a large chunk, most of them just want to keep on accumulating and holding.
And honestly, the advantage of having a target in mind means you will reach that goal and can exceed it, if need for it arises, the point is you've reached the goal. Budget may keep us defined on the fixed amount we have in mind, and we know the drill "the more Bitcoin we have in our portfolio = the value of profit we will expect in the long run"