I have bid list arranged as follows:

Job    Customer
A      Z
A      X
A      Y
B      Z
B      Y
B      F
B      C

Jobs may have more than one Customer.  I'd like to count how many
times customer Z bids the same jobs as customer Y.  Ideally, I'd like
to create a report from this data that automatically identifies the
customers that compete against each other.  This list is exported from
Access, so it may be able to do this easier in it's database form, but
I haven't found a way there either.

It is easier in Access.

Assume it's table: JOBS
What you need to do is to link the table to itself.
If you use the visual query editor:

1. Start the query editor

2. Load the table twice (it will appear as Jobs_1 as the second one)

3. Link on Job

4. Click on the Totals icon just under the menus (looks like a letter E)

5. Choose Customer from Jobs as 1st output

6 Click on Customer from Jobs_2 as 2nd output

7. Click on Jobs

8. In the totals line, under Jobs, choose COUNT

9. Under Customer in the Jobs_2 table, on the Criteria row, put in:
    >Jobs.Customer
    (or whatever your Jobs table is called).

10. Run it

Ratty

You can use the PivotTable feature in Excel. Here is the step by step
instructions. Please open the Excel spreadsheet when you try the
steps.

1. Select the whole list including the headers using your mouse
2. Click on Data > PivotTable and PivotChart Report
3. When the dialog box opens with Step 1 of 3, check the following options:
        Microsoft Excel list or database
        PivotTable
4. Click on Next
5. Click on Next for Step 2 of 3
6. Click on the Layout button in Step 3 of 3
7. Drag the Job button to the ROW area
8. Drag the Customer button to the COLUMN area
9. Drag the Job button to the DATA area
10. Click on OK
11. Click on Finish

You should have a new worksheet with the data arranged meeting your requirements.

I would create a new spread sheet containing the list of
bidders(customers).  I would then use the function countif in excel to
check for bidding the same project and relay the info to the new
spread sheet.

I will give easy solution MS Access itself. you need not import to Excel

In MS Access we can resolve this.A table called "Bidding" in that
columns are Job and customer.create Query Insert>Query>design view >
select the table> right click>select "SQL view". there u need paste
sql statment.

SELECT Count(*) AS ["NoOfTimes"]
FROM Bidding AS t1, Bidding AS t2
WHERE t1.job=t2.job And t1.customer=[&Customer1] And t2.customer=[&Customer2];

Run the Query(double click on ur Query)
while running it will ask customer1 and Customer2.just enter your
customer names.you will get required answer

thanks
Venu