Bulb-outs at bus stops are becoming a popular request among transit geeks—they extend the sidewalk out into the street and make it so the bus doesn't have to weave in and out of traffic in order to pick up passengers. Reducing the weaving action and removing the need to wait for automotive traffic to clear up as the bus gets underway also shortens the amount of time spent stationary or hardly moving, improving the experience for riders.
As with normal bus stops, business owners are quick to leap to concerns about parking. However, bulb-outs should actually have either zero or a net positive impact on the amount of available on-street parking—traditional bus stops need clearances for pulling in and pulling out, often about 20 feet. That's one reason why mid-block bus stops are so discouraged—they need both pull-in and pull-out space, thus taking away 40 feet of parking space in addition to the room needed for the bus itself.
If you're in a city that is contemplating bulb-outs, they are most likely also considering bus stop consolidation. Rather than stopping every one or two blocks, buses may start stopping every two to four blocks. Again, removing stops would most likely lead to a net gain in the amount of available parking.
As for bus stops that may be removed, it would make sense to add bicycle parking and/or bike-sharing stations in the new empty space.