My read is this:
1) As long as the Cotls are playing well, there's not going to be a drastic change in the RB situation. They'll continue to use both and ride the hot hand. Bradshaw carved up the Niners last week. If he starts gashing the Jags this week, he'll stay in the game just like last week.
2) As long as both are healthy, they'll use both. It'll never be much more than a 60/40 split one way or another unless one guy is running very well in a game while the other isn't (i.e. Bradshaw last week).
3) First and foremost, for Richardson's role to increase, he's got to learn the pass protection schemes. They will limit his snaps until they're confident he won't get Luck killed. Richardson's been on the team about a week. I'd say 1 to 2 more weeks before they're comfortable with him.
4) Regardless of how many touches Richardson gets, he should get consistent goalline looks. He's the power back here. Both he and Bradshaw got goalline looks last week, but the sense I got from the game was that they left Bradshaw in to get his late touchdown because if felt like he deserved it with how hard he ran. Generally speaking, I think most goalline looks go to Richardson.
5) For Richardson to really take hold of this job, he's got to show more than he showed in Cleveland. He's got to have some type of burst and average more YPC. If he is what he was in Cleveland, they'll continue to use both situationally
6) Bradshaw will almost certainly get hurt with any type of extensive workload.
I honestly think Richardson is going to be very hit or miss for the next few weeks. He's a TD threat, but if he doesn't score, you're not getting a lot from 12 carries, 48 yds and maybe 1 rec for 7 yds.
If the Colts weren't playing the Jags this week I'd honestly have given a lot of thought to benching him for Bilal Powell.
He'll get his opportunity as the season goes on, though, and as has been pointed out many times, Bradshaw likely gets hurt at some point. If he looks great as the bell cow back, they won't go back to Bradshaw as anything more than a change of pace.
When that happens though, who knows. I have no problem playing matchups week to week for now with Richardson, but I'd target him as a buy low because he should get a shot later in the season, and should be pretty productive. Could be money in the fantasy playoffs.