Bolden is a special teamer.
His positional designation as "RB" is nominal only, as is Slater's as "WR". They're given these designations merely because football has no official positional designation for "special teams coverage specialist" (Pro Bowl voting doesn't really count). If either one of them is playing significant snaps on Offense for multiple games, it means that the Pats have a dire injury situation on their hands. If/when that happens, their ST snaps are reduced commensurately.
When injury circumstances forced the Pats to play Bolden at RB in 2015, his ST snaps were significantly reduced. When Burkhead began playing significant snaps on Offense for the Ravens late last season, his special teams snaps were also significantly reduced.
Aside from OL and a TE (occasionally) blocking for FGs and extra point kicks, and aside from RBs or WRs returning kicks/punts, regular significant contributors on Offense play virtually zero special teams snaps - especially not on the units that defend against opponent returns or that block for Pats returners. Bolden gets the bulk of his game snaps on these ST units (19/game on ST, 0.9/game on Offense in 2016).
[NOTE: Develin has been a bit of an exception to this. And, a few times in past seasons, a WR, RB or TE has played significant ST coverage snaps for a few games during his rookie season.]
This holds true for all NFL teams. Virtually all of their "high-use" special teamers are defensive players. You can verify this by reviewing the detailed snap counts on Pro-Football-Reference.
So, Bolden won't be competing against RBs for a roster spot, just as Slater won't be competing against WRs for a roster spot. Neither ever really has. As always, both will be competing only against other special teams candidates for a roster spot.
At $3.15M, Burkhead is being paid to be a significant regular contributor on Offense. He was never going to "replace Bolden" on special teams.