There is no easy answer for dealing with Bermuda. Assuming you are talking about control of Bermuda in a fescue/bluegrass lawn, you have a number of options. Each has drawbacks. All told, suppression is achievable, but full eradication may not be.
Dig it out - but Bermuda can resprout any bit of rhizome or root left in the soil and it is labor intensive. This is probably the least effective method of control with established stands of Bermuda as roots can be in the soil several feet deep.
Use glyphosate (RoundUp) on it - but it's non selective and any overspray will effect your turf. The advantages of this method are that it's generally less expensive than selective options and it uses 1 product.
Use a selective herbicidal cocktail to selectively target the Bermuda - but it can be expensive as a number of products come in sizes that are more than the average homeowner needs. These herbicides can also interfere with overseeding depending on the timing of applications. The big advantage with using a selective option is that, when applied correctly, it shouldn't kill your turf.
As of a few years ago, selective option 1 was running about $30/1,000 sf and option 2 was running about $25/1,000 sf.
Option A: Apply Fenoxaprop + Triclopyr (Tenacity 4 oz/A + Turflon 32 oz/A ) starting in mid-May and apply every 3 weeks. Spot treat only. Make no more than for 8 treatments per year. Reduce triclopyr rate to 16 oz/A in spring and fall and do not add triclopyr in Mid-summer on KY bluegrass or Fine Fescue.
Option B: Apply Fenoxaprop + Triclopyr (Acclaim 28 oz/A + Turflon 32 oz/A) twice in spring and twice in fall at 3 weeks between treatment. Apply Mesotrione (Tenacity) 4 times during summer between the Acclaim/Turflon treatments. Apply every 3 weeks.
With all 3 of the chemical options, repeated applications will be needed and this will likely be a multi-year project.
For the many who suffer with this horrendous weed, please provide clarification on:
1) do the costs in your para 5 for "options 1 and 2" refer to the "options A and B" which follow?
2) is that cost of material, or include hired applicator?
3) is that cost per application or total treatment?
Sorry for the confusion Option A is 1 (~$30/1,000 sf) and B is 2 (~$25/1,00 sf)