I've raised a few beef calves on a bottle through the years, but they never seem to grow off nearly as well as dairy calves, and certainly not as good as a calf on pasture with his mama - and I'm not sure they've returned enough $$ to pay for the milk replacer and feed; probably would have come out ahead to take 'em to the salebarn and sell 'em as baby calves.
But, anyway, I handle 'em just like I do dairy calves - when they're consuming about 1.5-2.0 lbs of calf starter ration per day, you just stop the bottle/bucket, and up their grain ration. Usually, I've been able to wean somewhere between 4 and 6 weeks of age - the younger the better, because milk replacer feeding is the most costly and labor-intensive part of hand-raising calves.
Current recommendations for developing dairy heifers is no hay feeding before about 8 weeks, but free-choice access to all the good quality calf starter ration they can consume, up to 5-6#/day. Once they're weaned, I kick 'em out into a lot so they can graze, but they still get grain until 4-5 months of age, at which time they should have sufficient rumen development to grow well if pasture forages are high quality.
BTW 4 weeks is too young to ween as their rumen is not developed enough and you will end up with a runt.
Ween no less then 6 weeks, but really to have a good developed calf 3 months of at least 6 pints of milk twice a day and good leafy hay (or green grass) and a good dairy calf starter ration will leave you with a deep well developed calf that no one will know that you were the "mom". Ween and continue with a good TMR.
We have also cut hay out of the diet for the first 2 weeks and the end result was stunted expensive dairy heifer calves so that was discontinued in a hurry. The key to feeding hay early is to get the good stuff at least 17% protein ,usually 2nd or 3rd cut and small or large squares so there is still the leaves in the bales.
Please also note that if you are in a very hot climate the protein percentage of grain needs to be adjusted accordingly.